CHM320 PRACTICE EXAM #1 (SPRING 2018)

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1 CHM320 PRACTICE EXAM #1 (SPRING 2018) Name: Score: NOTE: You must show your work, with sufficient number of intermediate steps. No credit will be awarded if you simply write down the answers from memory or from guessing. All numerical answers MUST have proper units. 1. Are the following statements correct? Circle yes or no. [1 point each] (a) In photo-electric effect experiment, the kinetic energy of ejected electron increases if we increase the intensity (brightness) of the light. [yes no] (b) The heavier the particle is, the shorter the de Broglie wavelength becomes. [yes no] (c) In the Bohr model of hydrogen atom, the radius of stable orbit increases as the energy of electron increases. [yes no] (d) For a particle in a box, the probability to find the particle is always maximum at the center of the box. [yes no] (e) The uncertainty associated with the position and momentum of a particle can not be zero because the measuring device can never achieve perfect accuracy. [yes no] 2. Questions about the properties of photon: (a) Calculate the linear momentum of a photon of wavelength 350 nm. What speed does a hydrogen molecule need to travel to have the same linear momentum? (b) Calculate the energy of a photon and the energy of a mole of photons for the radiation with wavelength 400 nm (blue). 1

2 3. Briefly answer the following questions (One or Two sentences). (a) According to classical wave theory of light, how the kinetic energy of ejected electron in photo-electron effect should depend on the wavelength of light? (b) Explain why the wave nature of macroscopic object (like baseball) can be ignored. (c) What is the Bohr frequency rule? (d) What does normalization of wavefunction mean. (e) What are the boundary conditions for a particle in a box of length a? Explain why. (f) Sketch the wavefunctions of a particle in a box for the five lowest energy states. 2

3 4. The work function for metallic rubidium is 2.09 ev in photo-electric effect experiment. (a) Calculate the kinetic energy and the speed of electron ejected by the light with wavelength 195 nm. (b) What is the threshold wavelength (λ ) for rubidium? 5. Questions about de Broglie hypothesis. (a) Calculate the de Broglie wavelength of an He atom traveling at 1000 m/s (a tpyical speed at room temperature). (b) If the momentum of a photon is kg m/s, what is the energy of this photon in cm 1? 3

4 6. Questions about the Bohr model of hydrogen: (a) The Bohr model of hydrogen atom is based on the postulate that the angular momentum (l) of electron is quantized: l = n h. Show that the right hand side has the unit of angular momentum. (b) Using the relation given in part (a), calculate the velocity of electron in the n = 1 orbit. Note that the Bohr radius is 52.9 pm. How does it compare to the speed of light? (c) Calculate the longest wavelength possible in the Lymann series and the shortest wavelength in the the Balmer series. You will see that the latter is larger than the former. What does this tell us about the energy levels of hydrogen atom? 4

5 7. Consider a 1-dimensional particle in a box problem where the box is located between x = a/2 and x = +a/2, rather than 0 and a. (a) What are the boundary conditions for this system? (b) What are the wavefunctions for this PIB problem? You can get the answer from the ψ n (x) derived in class without solving the Schrodinger equation. Make sure the wavefunctions satisfy the boundary conditions mentioned in part (a). (c) By direct substition, show that the wavefunctions you mentioned in part (b) satisfy the Schrodinger equation. What are the energy levels for this PIB problem? Is the energy expression different from that of PIB problem discussed in class? 5

6 8. The UV absorption of 1,3,5-hexatriene occurs at 258 nm. (a) How many π electrons does this molecule have? (b) If π electrons are described by particle-in-a-box (PIB) model, what are the quantum numbers of two states involved in the UV transition of hexatriene? (c) Assuming that the particle-in-a-box (PIB) model is valid for π electrons, calculate the average C-C distance in 1,3,5-hexatriene that is consistent with the observed UV absorption wavelengh. (d) List possible sources error associated with the PIB model for the UV absorption of conjugated systems. 6

7 9. Consider the hypothetical one-dimensional hydrogan atom where the proton is located at the origin (x = 0) and the electron (with mass m) moves along a line (x > 0). The interaction between proton and electron follows the Coulomb s law: V(x) = e2 4πǫ 0 x (a) Set up the Schrodinger equation for the electron (b) A possible solution of Schrodinger equation in(a) has the following functional form: ψ(x) = xe ax, where a is a constant. Show by direction substition that Schrodinger equation becomes the following relation with the given wavefunction. ( ) a h 2 m e2 e ax = (E + a2 h 2 ) xe ax 4πǫ 0 2m 7

8 (c) The relation given in part (b) can be satisfied only if the quantities in parenthesis are zero (why?). Find the expression for a value and the corresponding energy E that makes the trial wavefunction an acceptible wavefunction for 1D hydrogen atom. 8

CHM320 EXAM #2 USEFUL INFORMATION

CHM320 EXAM #2 USEFUL INFORMATION CHM30 EXAM # USEFUL INFORMATION Constants mass of electron: m e = 9.11 10 31 kg. Rydberg constant: R H = 109737.35 cm 1 =.1798 10 18 J. speed of light: c = 3.00 10 8 m/s Planck constant: 6.66 10 34 Js