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《Chemical Physics:Molecular Clouds,Clusters,and Corrals》Dudley Herschbach

《Chemical Physics:Molecular Clouds,Clusters,and Corrals》Dudley Herschbach
《Chemical Physics:Molecular Clouds,Clusters,and Corrals》Dudley Herschbach

Chemical physics:Molecular clouds,clusters,and corrals

Dudley Herschbach

Department of Chemistry and Chemical Biology,Harvard University,

Cambridge,Massachusetts02138

Vignettes of three frontier areas illustrate the eclectic scope of modern chemical physics.(1) Radioastronomy has revealed a profusion of organic molecules in interstellar clouds,now attributed to sequences of exoergic,bimolecular ion-molecule reactions proceeding far from thermodynamic equilibrium.The organic profusion occurs because He?ions react far more readily with CO than with the much more abundant H2molecules.(2)Molecular clusters,generated by supersonic expansions, have become a favorite medium for study of reactions and spectra.Exemplary episodes are the discovery of carbon-60and kindred fullerene molecules and the observation of sharp rotational spectra of guest molecules in super?uid helium clusters.(3)New means to control molecular trajectories are being developed.These include spatial orientation or alignment by?eld-induced hybridization of rotational states,corralling(or trapping)molecules after collisional or mechanical quenching of translational kinetic energy,and laser control of photochemical reaction pathways.

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I.INTRODUCTION

In its modern incarnation,chemical physics as a?eld is generally regarded as having been born in1933,along with the The Journal of Chemical Physics.Its?rst editor, H.C.Urey,declared that‘‘the boundary...has been completely bridged...chemists and physicists have be-come equally serious students of atoms and molecules’’(Urey,1933).Among other evangelical founders were P. Debye,H.Eyring,G.B.Kistiakowsky,https://www.sodocs.net/doc/1b8523361.html,ngmuir,G. N.Lewis,L.Pauling,K.S.Pitzer,J.C.Slater,J.H.Van Vleck,and E.B.Wilson,Jr.Actually,Urey’s bridge was still rickety and had to stretch over a wide cultural gulf (Nye,1993).1A major impetus for the new journal was the fact that The Journal of Physical Chemistry refused to accept any purely theoretical paper(and continued to do so for another two decades).By1939,however, Slater had published his Introduction to Chemical Phys-ics,and by1942Wilson and Van Vleck had established at Harvard the?rst Ph.D.program in chemical physics. Over the next50years,means of elucidating molecular structure and dynamics developed enormously,by virtue of pervasive applications of quantum theory and experi-mental tools provided by physics,especially myriad spectroscopic methods.

Chemical physics and physical chemistry no longer differ appreciably,either in research journals or in aca-demic programs,now that computers and lasers have become ubiquitous.Yet creative tension persists at the interface of chemistry and physics.The chemist wants above all to understand why one substance behaves dif-ferently from another;the physicist wants to?nd disem-bodied principles that transcend the speci?c substances.

A chemical physicist thus sometimes stands awkwardly astride a widening intellectual abyss.However,often the duality of outlook provokes invigorating perspectives. This article takes a brief look at three frontier areas that offer such perspectives.Necessarily,these vignettes are idiosyncratic and impressionistic;only a few leading ref-erences and reviews can be cited,and many other fruit-ful areas are left out altogether.The chief aim is to ex-emplify the characteristic eclectic style of chemical physics,coupling theory and experiment,probing struc-tural and dynamical aspects,and ranging from ab initio rigor to heuristic extrapolation.

II.CHEMISTRY IN INTERSTELLAR MOLECULAR CLOUDS Over the past30years,radioastronomy has revealed a rich variety of molecular species in the interstellar me-dium of our galaxy and even others.Well over100mol-ecules have now been identi?ed in the interstellar gas or in circumstellar shells(Thaddeus et al.,1998).These in-clude H2,OH,H2O,NH3,and a few other small inor-ganic species,but most are organic molecules,many with sizable carbon chains involving double or triple bonds.To appreciate how surprising this proliferation of organic molecules is,we need to review some aspects of the interstellar environment.

A.Uniform radiation,multiform chemistry

As early as1941,optical absorption lines of the CN molecule were observed in an interstellar cloud that fronted a bright star,which served as the light source. The intensity ratio of lines originating from the ground level and?rst excited rotational levels provided the?rst evidence for the3°K cosmic background radiation,al-though not recognized as such until25years later(Thad-deus,1972).This background contains roughly99%of the electromagnetic energy in the known universe.It is now established as isotropic,blackbody radiation and

1Nye concludes that chemistry,as a discipline,preceded and

aided the establishment of physics as an academic and labora-

tory discipline.She points out that the term‘‘chemical physics’’

often appears in the titles and chapters of textbooks in the

latter half of the19th century.These treated heat,light,and

electricity as chemical agents,topics regarded as prefatory to

the core of chemistry dealing with properties and reactions of

inorganic and organic substances.

S411 Reviews of Modern Physics,Vol.71,No.2,Centenary19990034-6861/99/71(2)/411(8)/$16.60?1999The American Physical Society

attributed to a frigid whimper of radiation,still in ther-

mal equilibrium,from a primordial inferno,the Big

Bang.

The cosmic abundance of the elements is drastically

nonuniform.Hydrogen comprises over92%,helium

over6%;next come oxygen at0.07%,carbon at0.04%,

and nitrogen at0.009%.The average density within our

galaxy is only about one H atom per cubic centimeter.

Yet the density is about a hundredfold higher in what

are called diffuse interstellar clouds and up to a million-

fold higher in dark clouds.In diffuse clouds,such as

those in which the CN rotational states were found to be

in thermal equilibrium with the3°K background radia-

tion,a molecule collides with another(H2or He)only

once every two months or so.This led,in the early days

of radioastronomy,to the expectation that emission

spectra from rotational levels of any polar molecules in

the interstellar medium would be unobservable,because

collisions were much too infrequent to alter the rota-

tional temperature.

Such pessimistic anticipation was dispelled by the dis-

covery of molecular rotational emissions from dark

clouds(Rank et al.,1971).This discovery showed that

the gas density in many interstellar regions was actually

high enough to enable the population of rotational lev-

els to be governed more strongly by collisions than by

the background radiation.However,the observed mo-

lecular abundances departed enormously from estimates

derived by assuming chemical equilibrium.For instance,

next to H2,carbon monoxide is the most abundant in-

terstellar molecule(although typically down by a factor

of10?4or more).But thermodynamic calculations pre-

dict that under typical dark cloud conditions(20°K,

density of H2?105cm?3)at chemical equilibrium there would be fewer than one CO molecule in the volume

(1084cm3)of the observable universe.Likewise,the

prevalence of organic molecules containing many car-

bon atoms and relatively little hydrogen is inexplicable

by thermodynamics.

B.Synthesis of interstellar molecules

This situation led Klemperer(1995,1997)to propose

a nonequilibrium kinetic scheme for the synthesis of in-

terstellar molecules,to show how‘‘chemistry can,in the

absence of biological direction,achieve complexity and

speci?city.’’The scheme invokes sequences of exoergic,

bimolecular ion-molecule reactions.Extensive labora-

tory experiments have shown that these processes are

typically quite facile and uninhibited by activation en-

ergy barriers,unlike most gas-phase chemical reactions

not involving ions.Uninhibited reactions in two-body

collisions are the only plausible candidates for gas-phase

chemistry at the low density and temperature of an in-

terstellar cloud.The clouds also contain dust particles of

unknown composition.Formation of hydrogen mol-

ecules from atoms is probably catalyzed on the surface

of dust particles,but the host of other molecules seem

more likely to be produced by nonequilibrium gas-phase

kinetics.

The dark clouds where most interstellar molecules have been seen are immense,typically comprised of hy-drogen and helium with a million times the mass of our Sun.In our galaxy such clouds loom as huge dark blotches obscuring regions of the Milky Way.Ionization by the pervasive?ux of100-MeV cosmic rays seeds the

clouds with a little H2?and He?(about one ion per500 cm3),from which sprout many reaction sequences.

The H2?rapidly reacts with H2to form H3?which,as known from laboratory studies,itself readily transfers a

proton to many other molecular species.Most of the H3?is converted to HCO?,a very stable species.This pre-diction was a triumph for Klemperer’s model.Soon thereafter interstellar emission from a species dubbed Xogen,which had not yet been seen on earth,was shown to come from the HCO?ion.It has proved to be the most abundant ion in dark clouds and has even been observed in several distant galaxies.

Much else offers support for the kinetic model.For

instance,proton transfer from H3?to nonpolar molecules such N2and CO2converts them to polar species HN2?and HOCO?,which are capable of emitting rotational spectra.Again,laboratory observation of these spectra (Saykally and Woods,1981)con?rmed the detection of interstellar emissions from these species.

Most striking are offspring of the He?ions,which ex-emplify how chemical kinetics can produce paradoxical results.The extraction by He?of a hydrogen atom from H2,the most abundant molecule in interstellar clouds, would be very exoergic.Yet,for reasons described be-low,that reaction does not occur.Instead,He?reacts with CO,the second most abundant molecule,to form C?and O.The ionization of helium is almost quantita-tively transferred to C?,enhancing its concentration a thousandfold(by the He/CO abundance ratio).In turn, the C?ion reacts only feebly with H2(via radiative as-sociation),but reacts avidly with methane,CH4,and acetylene,C2H2,to launch sequences that build up many organic compounds,including chains punctuated with double and triple bonds.The paradoxical irony is that the mutual distaste of the simplest inorganic species, He?and H2,gives rise to the proliferation of complex organic molecules in the cold interstellar clouds.

C.Electronic structure and reaction speci?city

The three-electron system involving only helium and two hydrogen atoms offers a prototypical example for interpretation of chemical dynamics in terms of elec-tronic structure(Mahan,1975).As shown in ion-beam scattering experiments,the reaction

He?H2?→HeH??H is endoergic by0.8eV,but occurs readily if at least that amount of energy is supplied,ei-ther as relative kinetic energy of the collision partners or

as vibrational excitation of H2?.In contrast,the reaction He??H2→HeH??H is exoergic by8.3eV,but appears not to occur at all;the less exoergic pathway to form He?H??H has been observed,but its reaction rate is four orders of magnitude smaller than for comparable exoergic ion-molecule reactions.

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Figure 1provides an explanation,due to Mahan (1975),for the drastic difference in reactivity of He ?H 2

?and He ?

?H 2.Plotted are diatomic potential-energy curves for the reactants and products;these represent cuts through the triatomic potential-energy surfaces in the asymptotic entrance and exit channels.Consider ?rst the lowest-lying trio of separated atoms,He ?H ??H.Since both the reactants He ?H 2

?and the products HeH ?

?H correlate adiabatically to He ?H ??H,the reaction can be expected to proceed on a single triatomic potential-energy surface.

However,for the upper trio of atoms,He ??H ?H,this does not hold.The ground-state H 2diatomic poten-tial curve;1?g ?,which arises from bringing together two H atoms with antiparallel spins,represents a cut in the asymptotic reactant region through the potential surface for He ??H 2collisions.The corresponding cut in the product region,generated by bringing together He ??H,yields an excited singlet state that is totally repulsive,according to electronic structure calculations.Likewise,the accompanying excited triplet state with parallel spins is at best only very weakly bound.Accordingly,colliding He ??H 2is very unlikely to form a stable HeH ?mol-ecule.

As can be seen in Fig.1,in the asymptotic reactant region,the ground-state H 2(1?g ?)potential curve

crosses at about 1.1?that for H 2?(2

?u ?),a strongly repulsive state.When He ?approaches H 2,however,the resulting interaction induces these states to mix,as both

then acquire the same symmetry (A ?under the C S point group).The crossing thus evolves into an avoided inter-section (indicated schematically by dashes).If electron transfer occurs,the adiabatically formed products ini-tially are He ?H 2?(2

?u ?),which dissociate directly to He ?H ??H.

Exemplary of chemical physics,the profusion of or-ganic molecules tumbling in the heavens is linked to devilish details that govern an electron hopping between helium and hydrogen.

III.MOLECULAR CLUSTERS,SUPERSTRONG OR SUPERFLUID

The properties and interactions of molecules are often much in?uenced by the company they keep.Molecular clusters,generated by supersonic expansion of gas into a vacuum apparatus,have now become a favorite medium for the study of reactions and spectra.Such clusters,composed of from two to up to a billion molecules,offer means for interpolating between gaseous and condensed phases or solution chemistry (Castleman and Bowen,1996).Before considering two examples from this cornu-copian ?eld,we describe the key experimental tool that made it possible,the supersonic nozzle.

A.The versatile supersonic beam

The canonical physics literature on molecular beams,going back to Otto Stern and I.I.Rabi,stressed that the pressure within the source chamber should be kept low enough so that molecules,as they emerged from the exit ori?ce,did not collide with each other.In this realm of effusive or molecular ?ow,the emergent beam provides a true random sample of the gas within the source,un-distorted by collisions.Chemical physicists,in desperate need of intensity for studies of reactions in crossed beams,violated the canonical ideal by using much higher source pressures.Collisions within the ori?ce then produced hydrodynamic,supersonic ?ow.This realm,avidly explored by chemical engineers (Fenn,1996),proved to offer many advantages.

When a gas expands isentropically into a vacuum through a pinhole nozzle,the pressure and temperature both drop abruptly.The nozzle imposes collisional com-munication that brings the gas molecules to nearly the same direction and velocity.It also ef?ciently relaxes thermal excitation of molecular rotation and (less so)vibration.Thus not only is the intensity of a supersonic beam far higher than that from an effusive source,but the spreads in velocity and rotational states are mark-edly narrowed.The effective temperature for relative motion of molecules within such a beam is typically only a few °K.Moreover,by seeding heavy molecules in a large excess of light diluent gas,one can accelerate the heavy molecules to the exit velocity of the light gas.Translational energies much higher than are feasible with an effusive source can thereby be obtained,up to a few

eV.

FIG. 1.Potential-energy curves for the diatoms in the asymptotic reactant and product regions of the (He-H 2)?sys-tem.Since the energies of He and He ?are included,here the ground 1?g ?state of H 2lies above the states of H 2?.Note the

crossing of the curves for H 2(1

?g ?)and H 2?(2?u ?),which occurs in the reactant region of He ??H 2,but which becomes an avoided intersection (indicated by dashes)when all three atoms are close to each other.From Mahan,1975.

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Within the markedly nonequilibrium environment of a supersonic expansion,chemical interactions are liber-ated from thermodynamic constraints.In effect,in the free energy,?H-T?S,the entropy term?S is sup-pressed by the low internal temperature within the beam.Even a weakly favorable enthalpy term?H can then suf?ce to produce large yields of molecular clusters.

B.Balls and tubes of carbon

The discovery of carbon-60and kindred fullerene molecules ranks among the most important achieve-ments of chemical physics(Dresselhaus et al.,1996; Baum,1997).It also af?rms the value of fostering eclec-tic collaborations and the playful pursuit of curious ob-servations.The crucial ingredient was a technique,de-vised by Richard Smalley,to generate clusters from solid samples.This procedure uses a laser to vaporize mate-rial,enabling it to be entrained in a supersonic gas?ow. In the early1980s,several laboratories had adopted this technique,chie?y to study clusters of metals or semicon-ductor materials,of interest for catalysis or microelec-tronics.Among many curious results were features of a mass spectrum of carbon clusters from laser-vaporized graphite,published by a group at the Exxon laboratory as part of an Edisonian survey(Rohl?ng et al.,1984). For C40and larger clusters,only those with an even number of carbon atoms appeared,in a broad distribu-tion extending above C100.Especially prominent in the mass spectrum was the C60peak,about twice as tall as its neighbors.

What is now justly regarded as the discovery of C60 did not come until nearly a year later.Smalley’s group at Rice University was visited by Harry Kroto from Sussex, who had long pursued work on carbon-containing inter-stellar molecules.Kroto wanted to examine carbon clus-ters and their reactions with other molecules,in hopes of identifying candidates for unassigned interstellar spec-tra.Smalley was reluctant to interrupt other work,par-ticularly since vaporizing carbon would make the appa-ratus very dirty.Fortunately,hospitality and willing graduate students prevailed.On repeating the Exxon work,the Rice group found that,when conditions were varied,the C60peak became far more prominent.That result led them to play with models and propose as an explanation the celebrated soccer-ball structure,dubbed Buckminsterfullerene.It contains12pentagonal and20 hexagonal carbon rings,with all60atoms symmetrically equivalent and linked to three neighbors by two single bonds and one double bond.Soon other fullerene cage molecules were recognized,differing from C60by the addition or subtraction of hexagonal rings,in accord with a theorem proved in the18th century by Euler. These elegant structures,postulated to account for cluster mass spectra,remained uncon?rmed for?ve years.Then,in1990,it was not chemists but astrophysi-cists who found a way to extract C60in quantity from soot produced in an electric arc discharge.As well as enabling structural proofs,that discovery opened up to synthetic chemistry and materials science a vast new do-main of molecular structures,built with a form of carbon that has60valences rather than just four.It is striking, however,that despite the great stability of C60and its self-assembly after laser ablation or arc discharge of graphite,as yet all efforts to synthesize C60by conven-tional chemical means have failed.Such means,which operate under thermodynamic equilibrium conditions, evidently cannot access facile reaction pathways. Among the burgeoning families akin to fullerene mol-ecules are carbon nanotubes,?rst discovered by Sumio Iijima at NEC Fundamental Research Laboratories in Tsukuba,Japan.Particularly intriguing is a single-walled nanotube(designated10,10)of the same diameter as C60 (7.1?).In principle,its chicken-wire pattern of hexa-gons can be extended inde?nitely;in practice,nanotubes of this kind have now been made that contain millions of carbon atoms in a single molecule.The electrical con-ductivity of this hollow carbon tube is comparable to copper,and it forms?bers100times stronger than steel but with only only one-sixth the weight.Already carbon nanotubes have provided much enhanced performance as probe tips in atomic force microscopy.Chemically modifying the nanotube tips has even been shown to create the capability of chemical and biological discrimi-nation at the molecular level,in effect directly reading molecular braille(Wong et al.,1998).A host of other applications is in prospect.

C.Reactions and spectra in clusters

Much current work examines the effect of solvation on reaction dynamics or spectra by depositing solute re-actants or‘‘guests’’on a cluster of solvent or‘‘host’’molecules,bound by van der Waals forces or by hydro-gen bonds(Mestdagh et al.,1997).Often photoinduced reactions,particularly those involving electron or proton transfer,are studied in this way,as are processes involv-ing ion-molecule reactions within clusters(Castleman and Bowen,1996),including‘‘cage’’effects due to the solvent.Among many variants is work in which high-velocity clusters are made to collide with metal or crystal surfaces.Such collisions can induce even guest species that are ordinarily inhibited by a high activation barrier to react(Raz and Levine,1995).Here we consider a quite different special realm,employing spectra of a guest molecule to study clusters that are?nite quantum ?uids.

In the prototype experiment,shown in Fig.2,a super-sonic expansion generates large He or Ar clusters,each with103to105atoms.In?ight these clusters pick up one or more small guest molecules while passing through a gas cell,without suffering appreciable attenuation or de-?ection.The cluster beam is probed downstream by a laser,coaxial or transverse to the?ight path,and spec-troscopic transitions of the guest molecule are detected by laser-induced?uorescence or by beam depletion. This pickup technique,originally developed by Giacinto Scoles(Lehmann and Scoles,1998),is well suited to the study of unstable or highly reactive chemical species.In-deed,these may be synthesized in situ by using more

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than one pickup cell,or by introducing into the cell spe-cies generated in a discharge or pyrolytic decomposition.Instead,a stable guest molecule can serve to probe the environment within its solvent cluster.In this way,the

group of Peter Toennies at Go

¨ttingen (Hartmann et al.,1996;Grebenev et al.,1998)has recently obtained strik-ing results for super?uid helium clusters.

These 4He clusters are produced by a strong super-sonic expansion (e.g.,He at 5-bar pressure and 6.6°K behind a 5-?m nozzle),which drops the internal tem-perature to about 0.4°K,well below the transition tem-perature for super?uidity (T ??2.12°K).When a hot guest molecule comes aboard (from the pickup cell at 10?5mbar and ?300°K),the cluster rapidly evaporates away a few hundred He atoms,thereby cooling itself and the guest to the original internal temperature (in about 10?6sec).In the process,the guest molecule also migrates from the surface to the center of the cluster (as deduced from mass spectroscopic experiments and pre-dicted by theory).For a variety of guest species,among

them the linear triatomic molecule OCS,the Go

¨ttingen group found spectra with well-resolved rotational struc-ture.This indicates the guest molecules are rotating freely within the clusters,although with an effective mo-ment of inertia larger (by a factor of 2.7for OCS)than that for an isolated,gas-phase molecule.

In normal liquids,rotational structure in spectroscopic transitions is destroyed by diffusional and librational processes;free rotation is seen only for light,weakly interacting molecules such as H 2or CH 4.Free rotation within the 4He clusters thus can plausibly be attributed to super?uidity,but it might instead result from the ex-ceptionally cool and feeble guest-host interactions,fur-ther blurred by the large zero-point oscillations of the helium atoms.

As a diagnostic test for the role of super?uidity,the experiments were repeated using 3He clusters.These have lower density,so are more weakly interacting and somewhat colder (about 0.15°K),although far above the

super?uid range (T ??3?10?3°K).Indeed,in 3He clus-ters the OCS spectrum showed no rotational structure,but rather had the broad,featureless form typical for heavy molecules in normal liquids.A further elegant test was obtained in a series of runs made with increasing amounts of 4He added to the OCS vapor in the pickup cell.Because of their high diffusivity and lower zero-point energy,the 4He atoms entering a 3He cluster gath-ered around the guest molecule.The average number of such friendly 4He atoms that were picked up was esti-mated from a Poisson distribution.When this number reached about 60,the rotational structure in the OCS spectrum had again grown in,just as sharp as for pure 4

He clusters.

Thus,in the pure,nonsuper?uid 3He clusters,the guest molecule does not rotate freely,but it does so in pure,super?uid 4He clusters or when surrounded by about 60atoms of 4He,enough to form about two shells around the OCS molecule.Rough estimates suggest the increase in effective moment of inertia may be due chie?y to dragging along the vestigial normal-?uid com-ponent of these shells.The Go

¨ttingen experiments offer strong evidence that a sharp guest rotational spectrum is diagnostic of super?uidity and it can occur even in 4He clusters with as few as 60atoms.

IV.CORRALLING MOLECULES,CONTROLLING REACTIONS

Under ordinary experimental conditions,gas mol-ecules careen about in all directions with a broad range of thermal velocities and also tumble erratically with random spatial orientations.Taming that molecular wildness has been a major odyssey of chemical physics,still unfolding.It is part of a modern alchemical quest to exploit molecular dynamics in developing means to con-trol the outcome of chemical reactions.We review

some

FIG.2.Schematic diagram (omitting vacuum pumps)of molecular-beam apparatus for depletion spectroscopy of molecules embedded in helium clusters.The large clusters or droplets of He,formed in a supersonic nozzle,pick up a guest molecule while passing thorough a scattering chamber.En route to the mass spectrometric detector,the cluster is irradiated by a tunable,coaxial laser.When the laser is in resonance with the guest molecule,the absorbed energy induces evaporation from the cluster and a depletion in the mass spectrometer signal.From Hartmann et al.,1996.

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recent advances,including efforts towards achieving spa-tial trapping of molecules and utilizing lasers as the phi-losopher’s stone.

A.Pendular orientation and alignment

Although supersonic beams have long served to sub-due the translational wildness of molecules,until a few years ago there was no generally applicable technique for constraining the spatial orientation of a molecular axis.Without that capability,major directional features of collisional interactions were averaged out by molecu-lar rotation.The only previous method for producing beams of oriented molecules,developed in the late 1960s,used inhomogeneous electric focusing?elds to se-lect intrinsically oriented rotational states in which the molecular axis precessed rather than tumbled.This is an excellent method;it has made possible incisive studies of ‘‘head vs tail’’reaction probabilities in collisions with both gas molecules and surfaces.However,the method requires an elaborate apparatus and is only applicable to low rotational states of symmetric top molecules(or equivalent)that exhibit a?rst-order Stark effect.

A different method,much wider in chemical scope and far simpler to implement,exploits the low rotational temperatures attainable in supersonic beams.This method,introduced in1990,uses a strong homogeneous electric or magnetic?eld to create oriented or aligned states of polar or paramagnetic molecules(Loesch,1995; Friedrich and Herschbach,1996).In the presence of the ?eld,the eigenstates become coherent linear superposi-tions or hybrids of the?eld-free rotational states.These hybrids coincide with the familiar Stark or Zeeman states when the dipole and/or the moment of inertia is small or the?eld is weak;then the molecule continues to tumble like a pinwheel.When the interaction is suf?-ciently strong,however,the hybrids become librational; then the molecule swings to and fro about the?eld di-rection like a pendulum.Such pendular states can be produced for linear or asymmetric rotors as well as for symmetric tops.The magnetic version produces align-ment rather than orientation,2but is applicable to many molecules not accessible to the electric version;this in-cludes paramagnetic nonpolar molecules and molecular ions(which would just crash into an electrode if sub-jected to an electric?eld).Either version requires that the interaction of the molecular dipole with the external ?eld exceed the kinetic energy of tumbling;hence the key role of drastic rotational cooling by a supersonic expansion.

The experimental simpli?cation is major because a fo-cusing?eld(typically a meter long and expensive to fab-ricate)is not needed.Instead,the molecular beam is merely sent between the plates of a small condenser (usually about1cm2in area and a few mm apart)or between the pole pieces of a compact magnet.The uni-form?eld which creates the hybrid eigenstates need only extend over the small region in which the beam actually interacts with its target.

A kindred variety of pendular states can be produced by utilizing the induced dipole moment created by non-resonant interaction of intense laser radiation with the molecular polarizability(Friedrich and Herschbach, 1995a,1995b).This can produce alignment whether the molecule is polar,paramagnetic,or neither,as long as the polarizability is anisotropic.That is generally the case;for example,for a linear molecule the polarizabil-ity is typically about twice as large along the axis as transverse to it.Although the electric?eld of the laser rapidly switches direction,since the interaction with the induced dipole is governed by the square of the?eld strength,the direction of the aligning force experienced by the molecule remains the same.Experimental evi-dence for strong alignment arising from the polarizabil-ity interaction has been found in nonlinear Raman spec-tra(Kim and Felker,1997).

Pendular states make accessible many stereodynami-cal properties.Studies of steric effects in inelastic colli-sions or chemical reactions are a chief application(Loe-sch,1995).The ability to turn the molecular orientation on or off makes possible modulation of angular distribu-tions and other collision properties,thereby revealing anisotropic interactions not otherwise observable.In photodissociation of oriented molecules(Wu et al., 1994),pendular hybridization renders the laboratory photofragment distributions much more informative. For all applications,the spectroscopy of pendular states has an important role,as the?eld dependence of suit-able transitions reveals the extent of molecular orienta-tion or alignment.Other features arising from the hybrid character of pendular states also prove valuable in spec-troscopy,including the ability to tune transitions over a wide frequency range and to access states forbidden by the?eld-free selection rules.

B.Towards trapping molecules

The advent of powerful methods for cooling,trapping, and manipulating neutral atoms has led to dramatic achievements,including Bose-Einstein condensation of atomic vapor,an atom laser,atom interferometry,and atom lithography.Molecular physics yearns to follow suit.However,many optical manipulation methods that are effective for atoms fail for molecules because of the complexity of the energy-level structure,with its myriad vibrational and rotational components.Here we merely note some promising approaches to manipulating or trapping molecules,most not yet demonstrated experi-mentally.

In addition to its utility for molecular alignment,the polarizability interaction with an intense,directional la-ser?eld provides a lensing effect acting on the transla-tional motion of molecules.Seideman(1996,1997)has given a theoretical analysis showing how this arises.The interaction with the?eld produces molecular states,

2As usual,here axial anisotropy is designated orientation if it

behaves like a single-headed arrow and alignment if it behaves

like a double-headed arrow.

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‘‘high-?eld seekers,’’whose energy levels decrease as the?eld increases.This generates a force that moves the molecule towards the spatial region of highest laser in-tensity.Thereby focusing occurs,subject to dynamics and dependent on the ratio between the molecular translational kinetic energy and the maximum attractive ?eld-induced potential.In the strong-interaction limit, where that ratio becomes much less than unity,the mol-ecules can become trapped in the laser?eld(Friedrich and Herschbach,1995a,1995b).

An electrostatic storage ring for polar molecules has also been proposed(Katz,1997),modeled on a neutron storage ring.This would employ an inhomogeneous hexapolar toroidal?eld,within which molecules in‘‘low-?eld seeking’’states would be con?ned and follow orbits determined by their rotational state and translational ve-locity.Design calculations limited to practical param-eters indicate that storage lifetimes of the order of 103–104s can be expected.However,since the molecu-lar trajectories must bend to stay in the ring,only mol-ecules with low translational kinetic energy can be stored.

Whatever means are used to create an attractive po-tential region,molecular trapping requires a way to re-move enough kinetic energy so that the molecule cannot escape from that region.Since collisions between trapped molecules can redistribute rotational or vibra-tional excitation into translation,those internal modes need to be quenched also.Photoassociation of trapped atoms can produce trapped diatomic molecules,but must contend with small yields and a strong propensity for vibrational excitation in forming the molecules.Col-lisional relaxation by means of a cold buffer gas(Doyle et al.,1995)has worked well for loading atoms into a magnetic trap.Recently this technique has achieved a large yield(about108)of trapped CaH molecules (Weinstein et al.,1998).The best buffer gas is3He;it can be maintained by a dilution refrigerator at about 0.24°K,where its vapor density is5?1015cm?3,ample for collisional quenching.Since the helium interaction with any trap potential will be negligibly weak,it can be pumped away after cooling down the molecules.A dis-advantage is that the mean lifetime of a molecule in the trap is much shorter than the time required to remove the buffer gas.

A dizzying proposal for disposing of kinetic energy involves mounting a supersonic nozzle on a high-speed rotor,in order to cancel the velocity of the emerging molecules(Herschbach,1998a).Design calculations in-dicate that centrifuge action should enhance markedly the supersonic beam quality,thereby shrinking the ve-locity width and lowering the equivalent temperature for both relative translation and rotation to a few hundred m°K.Preliminary experiments,as yet at modest rotor speeds,con?rm that gas can indeed be introduced along the rotor axis and emerge from a whirling arm in a su-personic beam,with the expected velocity subtraction. This approach,if it proves feasible,would avoid cryo-genic technology and provide an intense source of mol-ecules deprived of kinetic energy.

If a suf?cient density of molecules can be con?ned,

the temperature of the trapped ensemble can be low-

ered much further by evaporative cooling(Doyle et al.,

1991).The aim is to get to the range of a few milli-

degrees Kelvin or below,where the de Broglie wave-

length exceeds the size of the molecule(e.g.,?de B ?20?for Cl2at10mK).This would give access to an exotic regime for chemical reactivity,governed by quan-

tum tunneling and resonances(Herschbach,1998b;For-

rey et al.,1998).It should be remarked that‘‘trapping,’’

although now a?rmly established term,is ridiculously

inappropriate.The tightest traps in prospect have linear

dimensions at least103times larger than molecules;that

is not a cage,but a roomy corral.

https://www.sodocs.net/doc/1b8523361.html,ser control of reaction pathways

In‘‘real world’’chemistry,reaction pathways and

yields have to be cajoled or conjured,by adjusting mac-

roscopic conditions(temperature,concentrations,pH)

or catalysts.Chemical physicists have sought genuine

control of molecular pathways(Zare,1998).For bimo-

lecular reactions,this has been done by varying the col-

lision energy,orientation,or vibrational excitation of re-

actant molecules or by selecting particular alignments of

excited electronic orbitals of atoms.For unimolecular

processes,which we consider brie?y,control has been

achieved by utilizing the coherence of laser light(Gor-

don and Rice,1997).This enables the outcome to be

governed by quantum interference arising from the

phase difference between alternate routes or by the tem-

poral shape and spectral content of ultrashort light

pulses.

The method employing phase control,?rst proposed

by Brumer and Shapiro(1986,1997),offers a molecular

analog of Young’s two-slit experiment.An upper state

of a molecule is simultaneously excited by two lasers,of

frequencies?n and?m,absorbing n photons of one color and m of the other,with n?m?m?n.This pre-pares a superposition of continuum eigenstates?n ??m that correlate asymptotically with different prod-uct channels.The coef?cients of the components of this superposition state are determined by the relative phases and amplitudes of the two lasers.Since the wave-lengths differ markedly,the light waves do not interfere, but the wave functions produced by them strongly inter-fere.The cross term in??n??m?2thus governs the product distribution,and the outcome can be controlled by varying the relative phases and amplitudes of the la-sers.This scheme has received several experimental demonstrations in which product yields from two com-peting channels exhibit large modulations,180°out of phase.

Another method,operating in the time domain,was

introduced by Tannor and Rice(1985).This employs a

sequence of ultrashort light pulses to create a wave

packet of molecular eigenstates.The frequencies,ampli-

tudes,and phases of the pulse sequence are tailored to

favor a particular outcome as the wave packet evolves in

time.By means of optimal control theory,the pulse

S417

Dudley Herschbach:Chemical physics Rev.Mod.Phys.,Vol.71,No.2,Centenary1999

shape and spectral content can be adjusted to maximize the yield of a desired product(Kosloff et al.,1989;Peirce et al.,1990).Moreover,with iterative feedback,the ex-perimenter can be taught by the molecule how best to tailor the light pulses(Judson and Rabitz,1992).The ?rst reports of such molecular instruction,aided by a computer-controlled pulse shaper,have recently ap-peared(Bardeen et al.,1997;Assion et al.,1998).These may portend an era in which chemical physicists,like chess masters,learn of many subtle moves beyond their imagination.

V.BENEDICTION

This quick glance at a bulging family album has pointed to just a few snapshots.Anyone who looks at Advances in Chemical Physics or Annual Reviews of Physical Chemistry or the Faraday Discussions or many other journals will quickly learn of remarkable work in reaction dynamics,femtosecond chemistry,single-molecule spectroscopy,surface chemistry,phase transi-tions,protein dynamics,electronic structure theory,and a host of other vigorous domains of chemical physics. Having left unmentioned or implicit so much landmark work,I can only hope for a holographic effect,wherein even fragments convey something of the enterprising spirit of the?eld.In my own experience,it has been exhilarating over nearly?ve decades to witness what has happened on Urey’s bridge.Another sentence from his preface of65years ago seems apt as an abiding creed or benediction for chemical physics:‘‘New and effective methods,experimental and theoretical,for the study of these units from which massive matter is composed, have developed largely from physical discoveries which at the time did not appear to have the importance to centuries-old chemical problems that they have since as-sumed.’’(Urey,1993).

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S418Dudley Herschbach:Chemical physics Rev.Mod.Phys.,Vol.71,No.2,Centenary1999

大学物理学下册答案第11章

第11章 稳恒磁场 习 题 一 选择题 11-1 边长为l 的正方形线圈,分别用图11-1中所示的两种方式通以电流I (其中ab 、cd 与正方形共面),在这两种情况下,线圈在其中心产生的磁感应强度的大小分别为:[ ] (A )10B =,20B = (B )10B = ,02I B l π= (C )01I B l π= ,20B = (D )01I B l π= ,02I B l π= 答案:C 解析:有限长直导线在空间激发的磁感应强度大小为012(cos cos )4I B d μθθπ= -,并结合右手螺旋定则判断磁感应强度方向,按照磁场的叠加原理,可计 算 01I B l π= ,20B =。故正确答案为(C )。 11-2 两个载有相等电流I 的半径为R 的圆线圈一个处于水平位置,一个处于竖直位置,两个线圈的圆心重合,如图11-2所示,则在圆心O 处的磁感应强度大小为多少? [ ] (A )0 (B )R I 2/0μ (C )R I 2/20μ (D )R I /0μ 答案:C 解析:圆线圈在圆心处的磁感应强度大小为120/2B B I R μ==,按照右手螺旋定 习题11-1图 习题11-2图

则判断知1B 和2B 的方向相互垂直,依照磁场的矢量叠加原理,计算可得圆心O 处的磁感应强度大小为0/2B I R =。 11-3 如图11-3所示,在均匀磁场B 中,有一个半径为R 的半球面S ,S 边线所在平面的单位法线矢量n 与磁感应强度B 的夹角为α,则通过该半球面的磁通量的大小为[ ] (A )B R 2π (B )B R 22π (C )2cos R B πα (D )2sin R B πα 答案:C 解析:通过半球面的磁感应线线必通过底面,因此2cos m B S R B παΦ=?= 。故正 确答案为(C )。 11-4 如图11-4所示,在无限长载流直导线附近作一球形闭合曲面S ,当曲面S 向长直导线靠近时,穿过曲面S 的磁通量Φ B 将如何变化?[ ] ( A )Φ增大, B 也增大 (B )Φ不变,B 也不变 ( C )Φ增大,B 不变 ( D )Φ不变,B 增大 答案:D 解析:根据磁场的高斯定理0S BdS Φ==? ,通过闭合曲面S 的磁感应强度始终为0,保持不变。无限长载流直导线在空间中激发的磁感应强度大小为02I B d μπ= ,曲面S 靠近长直导线时,距离d 减小,从而B 增大。故正确答案为(D )。 11-5下列说法正确的是[ ] (A) 闭合回路上各点磁感应强度都为零时,回路内一定没有电流穿过 (B) 闭合回路上各点磁感应强度都为零时,回路内穿过电流的代数和必定为零 (C) 磁感应强度沿闭合回路的积分为零时,回路上各点的磁感应强度必定为零 (D) 磁感应强度沿闭合回路的积分不为零时,回路上任意一点的磁感应强度 I 习题11-4图 习题11-3图

大学物理 马文蔚 第五版 下册 第九章到第十一章课后答案汇总

第九章振动 9-1一个质点作简谐运动, 振幅为A,在起始时刻质点的位移为 2 A -,且向x轴正方向运动,代表此简谐运动的旋转矢量为() 题9-1图 分析与解(b)图中旋转矢量的矢端在x轴上投影点的位移为-A/2,且投影点的运动方向指向O x轴正向,即其速度的x分量大于零,故满足题意.因而正确答案为(b).9-2已知某简谐运动的振动曲线如图(a)所示,则此简谐运动的运动方程为()()()()() ()()()() cm π 3 2 π 3 4 cos 2 D cm π 3 2 π 3 4 cos 2 B cm π 3 2 π 3 2 cos 2 C cm π 3 2 π 3 2 cos 2 A ?? ? ?? ? + = ?? ? ?? ? - = ?? ? ?? ? + = ?? ? ?? ? - = t x t x t x t x 题9-2图 分析与解由振动曲线可知,初始时刻质点的位移为–A/2,且向x轴负方向运动.图(b)是其相应的旋转矢量图,由旋转矢量法可知初相位为3/π 2.振动曲线上给出质点从–A/2 处运动到+A处所需时间为 1 s,由对应旋转矢量图可知相应的相位差3/π 4 Δ=,则角频率()1s3/π4 Δ / Δ- = =t ω,故选(D).本题也可根据振动曲线所给信息,逐一代入方程来找出正确答案.

9-3 两个同周期简谐运动曲线如图(a ) 所示, x 1 的相位比x 2 的相位( ) (A ) 落后2π (B )超前2 π (C )落后π (D )超前π 分析与解 由振动曲线图作出相应的旋转矢量图(b ) 即可得到答案为(b ). 题9-3 图 9-4 当质点以频率ν 作简谐运动时,它的动能的变化频率为( ) (A ) 2 v (B )v (C )v 2 (D )v 4 分析与解 质点作简谐运动的动能表式为()?ωω+=t A m E k 222sin 2 1,可见其周期为简谐运动周期的一半,则频率为简谐运动频率ν的两倍.因而正确答案为(C ). 9-5 图(a )中所画的是两个简谐运动的曲线,若这两个简谐运动可叠加,则合成的余弦振动的初相位为( ) (A ) π2 3 (B )π21 (C )π (D )0 分析与解 由振动曲线可以知道,这是两个同振动方向、同频率简谐运动,它们的相位差 是π(即反相位).运动方程分别为t A x ωcos 1=和()πcos 2 2+= t ωA x .它们的振幅不同.对于这样两个简谐运动,可用旋转矢量法,如图(b )很方便求得合运动方程为t A x ωcos 21=.因而正确答案为(D ).

物理学教程(第二版)-马文蔚下册公式原理整理(1)

物理期末知识点整理 1、 计算题知识点 1) 电荷在电场中运动,电场力做功与外力做功的总的显影使得带电粒子动能增加。 2) 球面电荷均匀分布,在球内各点激发的电势,特别是在球心激发的电势(根据高斯定理,球面内的电场强度为零,球内的电势与球面的电势相等 04q R επε= ,电势满足叠加原理) 3) 两个导体球相连接电势相等。 4) 载流直导线在距离r 处的磁感应强度02I B r μπ= ,导线在磁场中运动产生的感应电动势。(电场强度02E r λπε= )t φ ξ=- 5) 载流直导线附近的线框运动产生的电动势。 6) 已知磁场变化,求感应电动势的大小和方向。 7) 双缝干涉,求两侧明纹间距,用玻璃片覆盖其中的一缝,零级明纹的移 动情况。(两明纹间距为' d d d λ?= ,要求两侧明纹的间距,就是要看他们之间有多少个d ?,在一缝加玻璃片,使得一端的光程增加,要使得两侧光程相等,光应该向加玻璃片的一方移动) 8) 牛顿环暗环公式,理解第几暗环的半径与k 的关系。(r =k=0、1、2…..)) 9) 光栅方程,光栅常数,第几级主极大与相应的衍射角,相应的波长,每厘米刻线条数,第一级谱线的衍射角(光栅明纹方程(')sin b b k θλ+=±(k=0、1、2….)暗纹方程(')sin (21)/2b b k θλ+=±+(k=0、1、2….)光栅常数为'b b +) 10) 布鲁斯特定律,入射角与折射角的关系2 1 tan b n n θ= 2、 电场强度的矢量合成 3、 电荷正负与电场线方向的关系(电场线从正电荷发出,终止于负电荷) 4、 安培环路定理0Bdl I μ=?。 5、 导线在磁场中运动(产生感应电动势),电流在磁场中运动受到安培力的作用。 6、 干涉条件(频率相同,相位相等或相位差恒定,振动方向相同) b θ

大学物理第三版下册答案(供参考)

习题八 8-1 电量都是q的三个点电荷,分别放在正三角形的三个顶点.试问:(1)在这三角形的中心放一个什么样的电荷,就可以使这四个电荷都达到平衡(即每个电荷受其他三个电荷的库仑力之和都为零)?(2)这种平衡与三角形的边长有无关系? 解: 如题8-1图示 (1) 以A处点电荷为研究对象,由力平衡知:q'为负电荷 2 2 2 0) 3 3 ( π4 1 30 cos π4 1 2 a q q a q' = ? ε ε 解得q q 3 3 - =' (2)与三角形边长无关. 题8-1图题8-2图 8-7 一个半径为R的均匀带电半圆环,电荷线密度为λ,求环心处O点的场强. 解: 如8-7图在圆上取? Rd dl= 题8-7图 ? λ λd d d R l q= =,它在O点产生场强大小为

2 0π4d d R R E ε? λ= 方向沿半径向外 则 ??ελ ?d sin π4sin d d 0R E E x = = ??ελ ?πd cos π4)cos(d d 0R E E y -= -= 积分R R E x 000 π2d sin π4ελ ??ελπ == ? 0d cos π400 =-=? ??ελ π R E y ∴ R E E x 0π2ελ = =,方向沿x 轴正向. 8-11 半径为1R 和2R (2R >1R )的两无限长同轴圆柱面,单位长度上分别带有电量λ和-λ,试求:(1)r <1R ;(2) 1R <r <2R ;(3) r >2R 处各点的场强. 解: 高斯定理0 d ε∑? = ?q S E s 取同轴圆柱形高斯面,侧面积rl S π2= 则 rl E S E S π2d =?? 对(1) 1R r < 0,0==∑E q (2) 21R r R << λl q =∑ ∴ r E 0π2ελ = 沿径向向外

最新第五版大学物理答案(马文蔚)

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内蒙古科技大学马文蔚大学物理(下册)第六版答案解析

第九章振动 习题:P37~39 1,2,3,4,5,6,7,8,16.

9-4 一质点做简谐运动,周期为T,当它由平衡位置向X 轴正方向运动时,从1/2 最大位移处到最大位移处这段路程所需的时间( ) A、T/12 B、T/8 C、T/6 D、T/4 分析(C),通过相位差和时间差的关系计算。可设位移函数 y=A*sin(ωt),其中ω=2π/T; 当y=A/2, ω t1= π /6 ;当y=A, ω t2= π /2 ;△ t=t2-t1=[ π /(2 ω )]-[ π /(6 ω )]= π/(3ω)=T/6

9-回图(a)中所阿的是两个简谐运动的曲线,若这两个简谐j?动可叠加* 则合成的余弦振动的初相位为() 3 1 (A)-7W (B)—IT(C)F (D)O 分析与解由振动曲线可以知道,这是两个同振动方向、同频率简谐运动, 它们的相位差是TT(即反相位)?运动方程分别为X I= Acos ωt利%2= -^-CoS(((;? + 瓷)?它们的振幅不同.对于这样两个简谐运动M用旋转欠量送,如图(b)很方便 A 求得合运动方程为x=ycos ωt.因而正确答案为(D). 9-目有一个弹簧振子,振幅4 =2-0 X 10-2 m,周期T = 1.0 s,初相<p = 3ιτ∕4.试写出它的运动方程,并作出X - 1图I e - i图和a - t图. 解因3=X∕T,则运动方程 / 2πf ≡?cos(ωt + φ) =ACUS

根据题中给出的数据得 X = 2. 0 Xio '2cos( 2irf + O- 75τr) ( m ) 振子的速度和加速度分别为 t) = dx∕(It = -4π × 10^2Rin(2ττt + 0. 75ττ) (m * s^,) (Z = ?2χ∕df2 = - 8TT2X 10 ^2cos( 2τrt + 0. 75τT) ( m ? s ^2) X-I^V-C及Oft图如图所示.

大学物理_马文蔚__第五版_下册_第九章到第十一章课后答案

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9-3 两个同周期简谐运动曲线如图(a ) 所示, x 1 的相位比x 2 的相位( ) (A ) 落后2π (B )超前2 π (C )落后π (D )超前π 分析与解 由振动曲线图作出相应的旋转矢量图(b ) 即可得到答案为(b ). 题9-3 图 9-4 当质点以频率ν 作简谐运动时,它的动能的变化频率为( ) (A ) 2 v (B )v (C )v 2 (D )v 4 分析与解 质点作简谐运动的动能表式为()?ωω+=t A m E k 222sin 2 1,可见其周期为简谐运动周期的一半,则频率为简谐运动频率ν的两倍.因而正确答案为(C ). 9-5 图(a )中所画的是两个简谐运动的曲线,若这两个简谐运动可叠加,则合成的余弦振动的初相位为( ) (A ) π2 3 (B )π21 (C )π (D )0 分析与解 由振动曲线可以知道,这是两个同振动方向、同频率简谐运动,它们的相位差 是π(即反相位).运动方程分别为t A x ωcos 1=和()πcos 2 2+= t ωA x .它们的振幅不同.对于这样两个简谐运动,可用旋转矢量法,如图(b )很方便求得合运动方程为t A x ωcos 21=.因而正确答案为(D ).

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(C) 穿过S 面的电场强度通量不变,O 点的场强大小改变 (D) 穿过S 面的电场强度通量不变,O 点的场强大小不变 答案:D 解析:根据高斯定理,穿过闭合曲面的电场强度通量正比于面内电荷量的代数和,曲面S 内电荷量没变,因而电场强度通量不变。O 点电场强度大小与所有电荷有关,由点电荷电场强度大小的计算公式2 04q E r πε= ,移动电荷后,由于OP =OT , 即r 没有变化,q 没有变化,因而电场强度大小不变。因而正确答案(D ) 9-4 在边长为a 的正立方体中心有一个电量为q 的点电荷,则通过该立方体任一面的电场强度通量为 [ ] (A) q /ε0 (B) q /2ε0 (C) q /4ε0 (D) q /6ε0 答案:D 解析:根据电场的高斯定理,通过该立方体的电场强度通量为q /ε0,并且电荷位于正立方体中心,因此通过立方体六个面的电场强度通量大小相等。因而通过该立方体任一面的电场强度通量为q /6ε0,答案(D ) 9-5 在静电场中,高斯定理告诉我们[ ] (A) 高斯面内不包围电荷,则面上各点E 的量值处处为零 (B) 高斯面上各点的E 只与面内电荷有关,但与面内电荷分布无关 (C) 穿过高斯面的E 通量,仅与面内电荷有关,而与面内电荷分布无关 (D) 穿过高斯面的E 通量为零,则面上各点的E 必为零 答案:C 解析:高斯定理表明通过闭合曲面的电场强度通量正比于曲面内部电荷量的代数和,与面内电荷分布无关;电场强度E 为矢量,却与空间中所有电荷大小与分布均有关。故答案(C ) 9-6 两个均匀带电的同心球面,半径分别为R 1、R 2(R 1

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第三章 动量守恒定律和能量守恒定律 3-1质量为m 的物体,由水平面上点O 以初速为0v 抛出,0v 与水平面成仰角α。若不计空气阻力,求:(1)物体从发射点O 到最高点的过程中,重力的冲量;(2)物体从发射点到落回至同一水平面的过程中,重力的冲量。 分析:重力是恒力,因此,求其在一段时间内的冲量时,只需求出时间间隔即可。由抛体运动规律可知,物体到达最高点的时间 g v t αsin 01=?,物体从出发到落回至同一水平 面所需的时间是到达最 高点时间的两倍。这样, 按冲量的定义即可求出 结果。另一种解的方法是根据过程的始、末动量,由动量定理求出。 解1:物体从出发到达最高点所需的时间为 g v t αsin 01=?

则物体落回地面的时间为 g v t t αsin 22012=?=? 于是,在相应的过程中重力的冲量分别为 j j F I αsin d 0111 mv t mg t t -=?-==??,j j F I αsin 2d 0222 mv t mg t t -=?-==?? 3-2如图所示,在水平地面上,有一横截面2 m 20.0=S 的直角弯管,管中有流速为1s m 0.3-?=v 的水通过, 求弯管所受力的大小和方向。 解:在t ?时间内,从管一端流入 (或流出)水的质量为 t vS m ?=?ρ,弯曲部分AB 的水 的动量的增量则为 ()()A B A B v v t vS v v m p -?=-?=?ρ 依据动量定理p I ?=,得到管壁对这部分水的平均冲力()A B v v I F -=?=Sv t ρ 从而可得水流对管壁作用

力的大小为:N 105.2232?-=-=-='Sv F F ρ 作用力的方向则沿直角平分线指向弯管外侧。 3-3 A 、B 两船在平静的湖面上平行逆向航行,当两船擦肩相遇时,两船各自向对方平稳地传递kg 50的重物,结果是A 船停了下来,而B 船以 1s m 4.3-?的速度继续向前驶去。A 、B 两船原有 质量分别为kg 105.03?和kg 100.13 ?,求在传递重物前两船的速度。(忽略水对船的阻力) 题3.3分析:由于两船横向传递的速度可略去不计,则对搬出重物后的船A 与从船B 搬入的重物所组成的系统I 来讲,在水平方向上无外力作用,因此,它们相互作用的过程中应满足动量守恒;同样,对搬出重物后的船B 与从船A 搬入的重物所组成的系统II 亦是这样。由此,分别列出系统I 、II 的动量守恒方程即可解出结果。 解:设A 、B 两船原有的速度分别以v A 、v B 表示,传递重物后船的速度分别以v A 、v B 表示,被搬运重物的质量以m 表示。分别对上述系统I 、II 应用动量守

大学物理学第三版下册课后答案

习题八 8-1 电量都是q 的三个点电荷,分别放在正三角形的三个顶点.试问:(1)在这三角形的中心放一个什么样的电荷,就可以使这四个电荷都达到平衡(即每个电荷受其他三个电荷的库仑力之和都为零)?(2)这种平衡与三角形的边长有无关系? 解: 如题8-1图示 (1) 以A 处点电荷为研究对象,由力平衡知:q '为负电荷 2 220)3 3(π4130cos π412a q q a q '=?εε 解得 q q 3 3- =' (2)与三角形边长无 关. 题8-1图 题8-2图 8-2 两小球的质量都是m ,都用长为l 的细绳挂在同一点,它们带有相同电量,静止时两线夹角为2θ ,如题8-2图所示.设小球的半径和线的质量都可以忽略不计, 求每个小球所带的 解: 如题8-2图示 ?? ? ?? ===220)sin 2(π41 sin cos θεθθl q F T mg T e 解得 θπεθtan 4sin 20mg l q = 8-3 根据点电荷场强公式2 04r q E πε= ,当被考察的场点距源点电荷很近(r →0)时,则场强 →∞,这是没有物理意义的,对此应如何理解 ?

解: 02 0π4r r q E ε= 仅对点电荷成立,当0→r 时,带电体不能再视为点电荷,再用上式求 场强是错误的,实际带电体有一定形状大小,考虑电荷在带电体上的分布求出的场强不会是无限大. 8-4 在真空中有A ,B 两平行板,相对距离为d ,板面积为S ,其带电量分别为+q 和-q .则这两板之间有相互作用力f ,有人说f = 2 024d q πε,又有人说,因为f =qE ,S q E 0ε= ,所以f =S q 02 ε.试问这两种说法对吗?为什么? f 到底应等于多少 ? 解: 题中的两种说法均不对.第一种说法中把两带电板视为点电荷是不对的,第二种说法把合场强S q E 0ε= 看成是一个带电板在另一带电板处的场强也是不对的.正确解答应为一个板的电场为S q E 02ε=,另一板受它的作用力S q S q q f 02 022εε= =,这是两板间相互作用的电场力. 8-5 一电偶极子的电矩为l q p =,场点到偶极子中心O 点的距离为r ,矢量r 与l 的夹角为 θ,(见题8-5图),且l r >>.试证P 点的场强E 在r 方向上的分量r E 和垂直于r 的分量θE 分别为 r E = 302cos r p πεθ, θE =3 04sin r p πεθ 证: 如题8-5所示,将p 分解为与r 平行的分量θsin p 和垂直于r 的分量θsin p . ∵ l r >> ∴ 场点P 在r 方向场强分量 3 0π2cos r p E r εθ = 垂直于r 方向,即θ方向场强分量 3 00π4sin r p E εθ =

大学物理(第二版)下册答案-马文蔚剖析

物理学教程(二)下册 答案9—13 马文蔚 第九章 静 电 场 9-1 电荷面密度均为+σ的两块“无限大”均匀带电的平行平板如图(A )放置,其周围空间各点电场强度E (设电场强度方向向右为正、向左为负)随位置坐标x 变化的关系曲线为图 (B )中的( ) 题 9-1 图 分析与解 “无限大”均匀带电平板激发的电场强度为0 2εσ,方向沿带电平板法向向外,依照电场叠加原理可以求得各区域电场强度的大小和方向.因而正确答案为(B ). 9-2 下列说法正确的是( ) (A )闭合曲面上各点电场强度都为零时,曲面内一定没有电荷 (B )闭合曲面上各点电场强度都为零时,曲面内电荷的代数和必定为零 (C )闭合曲面的电通量为零时,曲面上各点的电场强度必定为零 (D )闭合曲面的电通量不为零时,曲面上任意一点的电场强度都不可能为零 分析与解 依照静电场中的高斯定理,闭合曲面上各点电场强度都为零时,曲面内电荷的代数和必定为零,但不能肯定曲面内一定没有电荷;闭合曲面的电通量为零时,表示穿入闭合曲面的电场线数等于穿出闭合曲面的电场线数或没有电场线穿过闭合曲面,不能确定曲面上各点的电场强度必定为零;同理闭合曲面的电通量不为零,也不能推断曲面上任意一点的电

场强度都不可能为零,因而正确答案为(B ). 9-3 下列说法正确的是( ) (A ) 电场强度为零的点,电势也一定为零 (B ) 电场强度不为零的点,电势也一定不为零 (C ) 电势为零的点,电场强度也一定为零 (D ) 电势在某一区域内为常量,则电场强度在该区域内必定为零 分析与解 电场强度与电势是描述电场的两个不同物理量,电场强度为零表示试验电荷在该点受到的电场力为零,电势为零表示将试验电荷从该点移到参考零电势点时,电场力作功为零.电场中一点的电势等于单位正电荷从该点沿任意路径到参考零电势点电场力所作的功;电场强度等于负电势梯度.因而正确答案为(D ). *9-4 在一个带负电的带电棒附近有一个电偶极子,其电偶极矩p 的方向如图所示.当电偶极子被释放后,该电偶极子将( ) (A ) 沿逆时针方向旋转直到电偶极矩p 水平指向棒尖端而停止 (B ) 沿逆时针方向旋转至电偶极矩p 水平指向棒尖端,同时沿电场线方向朝着棒尖端移动 (C ) 沿逆时针方向旋转至电偶极矩p 水平指向棒尖端,同时逆电场线方向朝远离棒尖端移动 (D ) 沿顺时针方向旋转至电偶极矩p 水平方向沿棒尖端朝外,同时沿电场线方向朝着棒尖端移动 题 9-4 图 分析与解 电偶极子在非均匀外电场中,除了受到力矩作用使得电偶极子指向电场方向外,还将受到一个指向电场强度增强方向的合力作用,因而正确答案为(B ). 9-5 精密实验表明,电子与质子电量差值的最大范围不会超过±10 -21 e ,而中子电量与零差值的最大范围也不会超过±10 -21e ,由最极端的情况考虑,一个有8个电子,8个质子和8个中子构成的氧原子所带的最大可能净电荷是多少? 若将原子视作质点,试比较两个氧原子间的库仑力和万有引力的大小. 分析 考虑到极限情况, 假设电子与质子电量差值的最大范围为2×10 -21 e ,中子电量为10-21 e ,则由一个氧原子所包含的8个电子、8个质子和8个中子可求原子所带的最大可能净电荷.由库仑定律可以估算两个带电氧原子间的库仑力,并与万有引力作比较. 解 一个氧原子所带的最大可能净电荷为 ()e q 21max 10821-??+= 二个氧原子间的库仑力与万有引力之比为 1108.2π46202max <

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