<p>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. </p><p>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</p><p>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.</p><p> b) What is 0, the work function, for the metal? Give your answer in units of eV.</p><p> c) What is max, the longest wavelength of light capable of ejecting electrons from the above metal? Give your answer in units of nm.</p><p>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.</p><p>3) The energy levels of the hydrogen atom are given by the equation</p><p>2 EH = - RH/n n = 1, 2, 3,... (3.1)</p><p>-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).</p><p>2 2 Ephoton = RH [ (1/nf ) – (1/ni ) ] (3.2)</p><p> 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.</p><p>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.</p><p>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.</p><p>-1 -1 molecule  (cm ) B (cm ) mH (amu) mX (amu) </p><p>1H19F 4138.3 20.956 1.008 18.998 1H35Cl 2991.0 10.593 34.969 1H81Br 2649.0 8.465 80.916</p>