Florida International University s11

CHM 3400 – Problem Set 10 Due date: Wednesday, April 17th. Late homework will not be accepted. NOTE: The final exam is Monday, April 22nd, from 5:00pm to 7:00pm, in PG5-155. It will be comprehensive.

A few useful conversion factors and constants: -19 -34 -31 1 eV = 1.602 x 10 J h = 6.626 x 10 Js me = 9.109 x 10 kg 1 amu = 1.661 x 10-27 kg c = 2.998 x 108 m/s

1) When light of wavelength  = 254. nm is used to illuminate a clean metal surface, the maximum kinetic energy of the electrons ejected from the metal is EK(max) = 3.18 eV. a) What is the maximum speed of the ejected electrons? Give your answer in units of m/s.

b) What is 0, the work function, for the metal? Give your answer in units of eV.

c) What is max, the longest wavelength of light capable of ejecting electrons from the above metal? Give your answer in units of nm.

2) The conversion efficiency of a lightbulb represents the fraction of the electrical power that the bulb converts into visible light. It is thus a measure of the effectiveness of the bulb as a light source. Due to their greater efficiency in converting electrical power into visible light, compact fluorescent lightbulbs (CFLs) have replaced incandescent lightbulbs (ILs) as light sources. Consider a 100. watt ( = 100. J/s) lightbulb. Calculate the number of photons per second emitted by a) A CFL (conversion efficiency = 8%) b) An IL (conversion efficiency = 2%) For ease in calculation, assume that all of the emitted photons have a wavelength  = 500. nm, roughly the center of the visible region of the spectrum.

3) The energy levels of the hydrogen atom are given by the equation

2 EH = - RH/n n = 1, 2, 3,... (3.1)

-1 where RH is the Rydberg constant, with RH = 109677 cm . a) Starting with eq 3.1, derive the following equation for the energy of a photon emitted by a hydrogen atom with initial quantum number ni, to move to a state with final quantum number nf (note ni > nf).

2 2 Ephoton = RH [ (1/nf ) – (1/ni ) ] (3.2)

b) The Balmer series is a series of light emissions in the visible region of the spectrum, corresponding to hydrogen atoms making the transition from an initial state with quantum number n i to a final state with quantum number nf = 2. Find the wavelength of light corresponding to the Balmer series emissions with n i = 3, 4, 5, 6, and . Give your wavelengths in nm.

4) The rotational constants for several hydrogen halides are given below. Based on this information do the following a) Find re, the equilibrium bond length, for each H – X bond. Give your answer in units of nm. b) Are the bond lengths consistent with your expectations? Explain.

5) The vibrational constants for several hydrogen halides are given below. Based on this information do the following: a) Find k, the force constant, for each H – X bond. Give your answer in units of N/m. b) Are the force constants consistent with your expectations? Explain.

-1 -1 molecule  (cm ) B (cm ) mH (amu) mX (amu)

1H19F 4138.3 20.956 1.008 18.998 1H35Cl 2991.0 10.593 34.969 1H81Br 2649.0 8.465 80.916