2021 量子化学(南京大学) 最新满分章节测试答案

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本课程起止时间为:2021-03-31到2021-06-13

Chapter 1 The Dawn of the Quantum Theory Test 1 The Dawn of the Quantum Theory

1、 问题:Which of the following phenomena does not represent the wave property of the light?
选项：
A: Interference of light.
B:Diffraction of light.
C:Polarization of light.
D:Photoelectric effect.
答案: 【Photoelectric effect.】

2、 问题:Why is Planck known as the father of quantum mechanics?
选项：
A:Find the phenomenon of radiation from heated objects.
B: Propose the concept of photon.
C:Propose the discontinuity of radiation energy.
D:Found the matrix mechanics.
答案: 【Propose the discontinuity of radiation energy.】

3、 问题:Calculate the first line of the hydrogen atom in the Lyman Series () using Rydberg formula (convert it to wavelength )
选项：
A:121.6 nm
B:91.2 nm
C:364.7 nm
D:656.5 nm
答案: 【121.6 nm】

4、 问题:Which of the following is not true for hydrogen atom ?
选项：
A:The frequency of the lines versus  is linear in hydrogen atom spectrum. 
B: As  the lines come closer and closer.
C:The wavelength of the lines versus  is linear in hydrogen atom spectrum.
D:Lines belong to the same series in hydrogen absorption spectrum have the same initial state.
答案: 【The wavelength of the lines versus  is linear in hydrogen atom spectrum.】

5、 问题:If the kinetic energy of an electron is increased by 21%,what is the percentage change in its de Broglie wavelength? 
选项：
A:21%
B:10%
C:5.2%
D:9.1%
答案: 【9.1%】

6、 问题:Which of the following statements is True?
选项：
A:According to Heisenberg’s uncertainty Principle, we can not know any two properties of a system simultaneously.
B:If we improve our instruments and experiment technique, we can simultaneously detect the position and velocity of the molecule fullerene 
C:Due to the uncertainty principle, it is impossible to predict the evolution of a system with time.
D:If the lifetime () of an excited state is very short, the peak of spectrum () will be very broad.
答案: 【If the lifetime () of an excited state is very short, the peak of spectrum () will be very broad.】

7、 问题:What are the assumptions in Bohr’s hydrogen atom model?
选项：
A:The electron has a stable orbit around the nucleus.
B:When an electron rotates around the nucleus, it radiates electromagnetic waves due to the constant change of its velocity.
C:The energy and the the angular momentum of an electron is quantized.
D:The motion of an electron can be described by a wave function.
答案: 【The energy and the the angular momentum of an electron is quantized.】

8、 问题:Which of the following are Einstein’s hypotheses for explaining the photoelectric effect?
选项：
A:Light consists of indivisible particles called photons with energy and momentum.
B:The energy of light is proportional to the square of the amplitude.
C:The energy of a photon is proportional to its frequency.
D:, where T is the kinetic energy of excited electrons on the surface of metal, and W is the work function of the metal.
答案: 【, where T is the kinetic energy of excited electrons on the surface of metal, and W is the work function of the metal.】

【作业】Chapter 1 The Dawn of the Quantum Theory Exercise 1 The Dawn of the Quantum Theory

小提示:本节包含奇怪的同名章节内容

1、 问题:Show that at low frequencies, Planck’s blackbody formula can be approximated by the Rayleigh-Jeans formula. Hint: Look up the Taylor series expansion of  in powers of .
评分规则: 【
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2、 问题:The work function of very pure Na is 2.75 eV, where(a) Calculate the maximum kinetic energy of photoelectrons emitted from Na exposed to 200 nm ultraviolet radiation. (b) Calculate the longest wavelength that will cause the photoelectric effect in pure Na. (c) The work function of sodium that has not been very carefully purified is substantially less than 2.75 eV, because of adsorbed sulfur and other substances derived from atmospheric gases. When impure Na is exposed to 200-nm radiation, will the maximum photoelectron kinetic energy be less than or greater than that for pure Na exposed to 200 nm radiation?
评分规则: 【
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3、 问题:A ground-state hydrogen atom absorbs a photon of light that has a wavelength of 97.2 nm. It then gives off a photon that has a wavelength of 486 nm. What is the final state of the hydrogen atom?
评分规则: 【
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4、 问题:Calculate that:(a) the wavelength and kinetic energy of an electron in a beam of electrons accelerated by a voltage increment of 100 V;(b) the kinetic energy of an electron that has a de Broglie wavelength of 200 pm (1 picometer = m).
评分规则: 【
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5、 问题:Show that the speed of an electron in the nth Bohr orbit of a hydrogen-like ion with a nuclear charge is . Calculate the values of for the first Bohr orbit for and .
评分规则: 【
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6、 问题:Calculate the de Broglie wavelength for (a) an electron with a kinetic energy of 100 eV, (b) a proton with a kinetic energy of 100 eV, and (c) an electron in the first Bohr orbit of a  hydrogen atom.
评分规则: 【
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7、 问题:An electron is confined to a linear region with a length of the same order as the diameter of an atom (about 100 pm). Calculate the minimum uncertainties in its speed. (a quantitative version of uncertainty relationship is  )
评分规则: 【
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8、 问题:An electron is confined to a linear region with a length of the same order as the diameter of an atom (about 100 pm). Calculate the minimum uncertainties in its speed. (a quantitative version of uncertainty relationship is  )
评分规则: 【
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Chapter 2 The Postulates and General Principles of Quantum Mechanics Test 2 The Postulates and Gener

1、 问题:Which of the following is not required for a function to be well-behaved wave function？
选项：
A:It has to be continuous.
B:It has to have the same value for an angular variable α and for α + 2π.
C:It must not tend to infinity.
D:It must be a real function.
答案: 【It must be a real function.】

2、 问题:Which of the following can be the definition of a Hermitian operator (f and g are arbitrary functions)?
选项：
A:
B:
C:
D:
答案: 【】

3、 问题:For a Hermitian operator and all functions ψi from its domain, one has:
选项：
A:
B:
C:
D:
答案: 【】

4、 问题:Which of the following is not the property of Hermitian operators?
选项：
A:The eigenvalues of a Hermitian operator are real.
B:The eigenvectors of a Hermitian operator are orthogonal.
C:The product of two Hermitian operators must be Hermitian.
D:The sum of two Hermitian operators must be Hermitian.
答案: 【The product of two Hermitian operators must be Hermitian.】

5、 问题:If the two operators and commute with each other, which of the following statement is not True:
选项：
A:Any eigenfunction of represents also an eigenfunction of .
B:One can choose a common set of functions, that are eigenfunctions of and .
C:Their corresponding observable quantities have simultaneously well-defined values.
D:
答案: 【Any eigenfunction of represents also an eigenfunction of .】

6、 问题:Which of the following statement about Time-independent Schrödinger equation is not true?
选项：
A:It is satisfied by a wave function that is an eigenfunction of the Hamiltonian of the system.
B:Any solution of this equation corresponds to a physically acceptable state of the system.
C:An eigenvalue may correspond to several linearly independent eigenfunctions.
D:Energy levels represent eigenvalues of this equation.
答案: 【Any solution of this equation corresponds to a physically acceptable state of the system.】

7、 问题:Which of the following statement about time-dependent Schrödinger equation is not true?
选项：
A:It describes the evolution in time of any quantum state.
B:It takes the form: .
C:It allows to calculate the time derivative of a wave function from its spatial-coordinate dependence at a fixed time.
D:If does not depend on time, its solution reads as .
答案: 【It takes the form: .】

8、 问题:Which of the following statement is True?
选项：
A: is an eigenvalue of the position operator .
B: is an eigenfunction of the position operator
C:The position operator is a linear operator.
D:The operator is a linear operator.
答案: 【The position operator is a linear operator.】

9、 问题:Which of the following statement is not True?
选项：
A:The product of two linear operators is a linear operator.
B:The product of two Hermitian operators is an Hermitian operator.
C:The sum of two linear operators is a linear operator.
D:The sum of two Hermitian operators is an Hermitian operator.
答案: 【The product of two Hermitian operators is an Hermitian operator.】

10、 问题:If and are both Hermitian, which of the following operator is not necessarily Hermitian?
选项：
A:
B:
C:
D:
答案: 【】

11、 问题:Which of the following statement is True ?
选项：
A:Two linearly independent eigenfunctions of the same Hamiltonian is always orthogonal to each other.