**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.**

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**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).**

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**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.**

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**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?**

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**Problem 5:**

**a. A possible eigenfunction for the system is:**

**Show that , 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.**

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**Problem 6:**

**Prove that momentum operator corresponding to is a Hermitian operator.**

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**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?**

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**第二章：**

**Problem 1:**

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

**A Hydrogen atom is in its 4***d* 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

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**Problem 2:**

**The spin functions ****a**** and β can be expressed as **

** and **

**The spin operator can be represented by**

**Show that **

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**Problem 3:**

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

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**Problem 4:**

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

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**Problem 5:**

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

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**Problem 6:**

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

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**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?**

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**Problem 8:**

**Using the trial eigenfunction for 0****£**** ***x* **£**** ***a * 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.

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**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**

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**第四章****: 4 - 7, 23, 24, 28**

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**第五章****: 5 - 18, 24, 29, 39**

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**第七章**** ****7 - 5****、****13****、****16****、****26****、****29**