物理化学A(I)作业习题

物理化学A(I) (教材第一至第九章)

第一章：

Problem 1:

a) Use the fact that to show that the radiant energy emitted per second by unit area of a blackbody is.

b) The sun’s diameter is m and its effective surface temperature is 5800 K. Assume the sun is a blackbody and estimate the rate of energy loss by radiation from the sun.

c) Use to calculate the relativistic mass of the photons lose by radiation from the sun in a year.

Problem 2:

The work function of K is 2.2eV and that of Ni is 5.0eV.

a) Calculate the threshold frequencies and wavelengths for these two metals.

b) Will violet light of wavelength 4000A cause the photoelectric effect in K? In Ni?

c) Calculate the maximum kinetic energy of the electron emitted in b).

Problem 3:

On the basis of the Bohr theory, calculate the ionization energy of the hydrogen atom and the linear velocity of an electron in the ground state of the hydrogen atom.

Problem 4:

What is the de Broglie wavelength of an oxygen molecule at room emperature? Compare this to the average distance between oxygen molecules in a gas at 1 bar at room temperature.

What is the de Broglie wavelength of an electron that has been accelerated through a potential difference of 100V.

What is the width in energy domain of a 4fs pulse?

Problem 5:

a. A possible eigenfunction for the system is:

Show that *ψψ , the probability, is independent of time.

b. Prove that m must be the integral in order for the function

to be an acceptable wave function.

Problem 6:

Prove that momentum operator corresponding to is a Hermitian operator.

Problem 7:

What is the degree of the degeneracy if the three quantum numbers of a three-dimensional box have the values 1, 2 and 3?

Calculate the lowest possible energy for an electron confined in a cube of sides equal to a) 10pm and b)10-15m. The latter cube is the order of the magnitude of an atomic nucleus; what do you conclude from the energy you calculate about the probability of a free electron being present in a nucleus?

第二章：

Problem 1:

Use hydrogenic orbitals to calculate the mean radius of a 1s orbital.

A Hydrogen atom is in its 4d state. The atom decays to a lower state by emitting a photon. Find the possible photon energies that may be observed. Give your answers in eV

)

/2exp(),,(),,,( iEt z y x t z y x πψ-=ψφ

m sin =Φx

p ?

Problem 2:

The spin functions α and β can be expressed as

and

The spin operator can be represented by

Show that

Problem 3:

Show that the Slater determinants for Helium atom and Lithium atom.

Problem 4:

Estimate the effective nuclear charge for a 1s electron in He, if the first ionization energy of helium is 24.6eV.

Problem 5:

Estimate the effective nuclear charge felt by the 2s electron in the lithium atom, if the ionization energy is 5.83eV

Problem 6:

Show the atomic term symbols for Helium and Nitrogen in their ground states.

Problem 7:

What is the spectroscopic term of the ground state of the Li atom? If the 2s electron is excited to the 2p state, what terms are then possible?

Problem 8: ??????=01α??

????=10β??

????-=100121?z S αα21?=z S ββ21?-=z S

for 0≤ x ≤ a Using the trial eigenfunction

and otherwise, compute the variational energy for a particle of mass m in an infinite potential well of width a . N is the normalization constant.

第三章

Problem 1:

Carry out a linear variation calculation for a particle of mass m in e-dimensional infinite potential well of width l . use and as trial eigenfunction. Compare the result with the exact ground- state energy. 3 – 2，4，6，12，13，24，27，30

第四章: 4 - 7, 23, 24, 28

第五章: 5 - 18, 24, 29, 39

第七章 7 - 5、13、16、26、29 )(x a Nx -=ψ0=ψ321x x l -=ψ7522

x x l -=ψ