CHEM 342. Spring 2002.  Next PS  Answers  PS#1.doc (Word 97)  

Problem Set #1

 

Note: Relevant Chapters in Mortimer are Chapters 14 and 15.

For the first three problems, please circle the correct answer.

Compton Effect

1. The Compton Effect was first observed by studying the scattering of X-rays by a graphite target. Although the incident X-rays were monochromatic, the scattered X-rays contained an additional component of shorter, same, longer wavelength.

 

Photoelectric Effect

2. If the frequency of incident light is above the threshold frequency, then as the intensity of light increases, the kinetic energy of ejected electrons decreases, remains constant, increases and the number of electrons decreases, remains constant, increases.

3. If the frequency of incident light is above the threshold frequency, then as the frequency of light increases, the kinetic energy of ejected electrons decreases, remains constant, increases and the number of electrons decreases, remains constant, increases.

4. What is the effect of incident light striking a metal surface if the frequency of the light is below the threshold frequency for this metal?

5. Define in a maximum of 20 words for each Correspondence Principle; Compton Effect; Photoelectric Effect.

6. The work function for metallic cesium is 3.43 ´ 10-19 J. Calculate the kinetic energy and the speed of the electrons ejected by light of 300 nm wavelength. [Hint: Planck's constant, h,is 6.626 ´ 10-34 J s; the speed of light in a vacuum, c, is 3.00 ´ 108 m/s; the mass of an electron, me, is 9.109 ´ 10-31 kg]

 

Blackbody Radiation

7. The peak of the Sun's emission occurs at about 480 nm. Estimate the temperature on its surface. Hint: The Wien displacement law reduces to , where the constant

 

Bohr Atom: Spectral Lines

8. Calculate the wavelength of light emitted when an electron falls from the n = 100 to the n = 99 orbit of the hydrogen atom. [Hint: Rydberg's constant, R, is 1.097 ´ 107 m-1]

 

DeBroglie Waves

9. Electrons are accelerated by a 1000 V potential drop. Calculate the de Broglie wavelength. Also calculate the wavelength of the X-rays that would be produced when these electrons strike a solid. [Hint:The electron charge is 1.602 ´ 10-19 C; the mass of an electron, me, is 9.109 ´ 10-31 kg; Planck's constant, h,is 6.626 ´ 10-34 J s.]

 

Well-Behaved Wave Functions

10. List the characteristics of a well-behaved wave function.

11. Which of the following functions are well-behaved? For those functions that are not well-behaved, explain why not.

    1. f(x) = x for , and f(x) = 0 for
    7. for , and f(x) = 0 for and for

12. A particle can move only along the x-axis and has a wave function . Give the expression for

  1. , the complex conjugate of (express answer in terms of k and x)
  2. P, the probability density (express answer in terms of and )
  3. the probability that the particle is between x1 and x2 (in terms of and ). Hint: You only need to set up the appropriate integral.

For any normalized , what is the probability that the particle is between and ? [Hint: this question has a numerical answer.]

 

Harmonic Oscillators: Hermite Polynomials

13. Calculate the zero-point energy of a harmonic oscillator consisting of a particle of mass 2.33 ´ 10-26 kg and force constant 155 N/m. [Hint: Planck's constant, h,is 6.626 ´ 10-34 J s.]

14. For the harmonic oscillator, substitute the wave function for the ground state into the Schrodinger equation and derive the expression for the ground state energy (also known as the zero-point energy). Hint: The wave function for the ground state is where . The expression for the ground state energy is where is the frequency.

15. In the vibrational motion of HI, the iodine atom essentially remains stationary because of its large mass. Assuming that the hydrogen atom undergoes harmonic motion and that the force constant k is 317 N/m, what is the fundamental vibration frequency . [Hint: The mass of a proton is 1.67 ´ 10-27 kg.]

PLEASE NOTE

  • The work you hand in should be neat and well organized, and it should show the strategy and steps you used in solving the problems, as well as the bottom-line answers (or solutions). In grading the problems, both your work-up and your final answers/solutions will be examined and evaluated.
  • The work handed in for grading must carry a pledge that the work is entirely yours and was done without any collaboration with other persons (except for the course instructor and TA's). You are encouraged to work with others in doing the exercises and problems found in the textbook, but all work handed in for grading should be done independently.