# Calculate the frequency and wavelength associated with a transition

Chemistry 260/261 Problem Set 1 — Due Wednesday Jan. 20 by 3 pm Winter 2016 1. Calculate the energy associated with a quantum (photon) of light with a wavelength of 825 nm. 2. Calculate the frequency and wavelength associated with a transition from the n=2 to n=3 Bohr levels of hydrogen. 3. Calculate the number of photons emitted by a 100 W yellow lamp (? = 560 nm) in 10.0 seconds assuming 100% efficiency. 4. The work function of rubidium is 2.09 eV. Can blue light (? = 470 nm) eject electrons from this metal? 5. It is observed experimentally that when light of wavelength longer than 564 nm shines on a surface of potassium metal no electrons are ejected from the metal. (a) What is the work function of potassium in eV? (b) What is the speed of the ejected electrons when light with a wavelength of 410 nm is used? (c) What is the de Broglie wavelength of these ejected electrons? 6. Wilhem Wien demonstrated that for blackbody radiation the product T ?max = constant (where T is absolute temperature). According to Planck’s expression this constant is hc/4.965kB. Sirius one of the hottest known stars has a black body spectrum with ?max = 260 nm. Use Wien’s law to estimate the surface temperature of Sirius. 7. Consider a particle of mass m that moves along the x axis under the influence of a potential energy of the following form: V ( x) =1 2kx jx 32What is the force experienced by the particle as a function of the position x? Write down the classical equation of motion that dictates the dynamics of the particle. 8. How fast would a buckyball (C60) travel to have a wavelength of 300 nm? Is this possible? Explain your answer. 9. Spectral lines of the Lyman and Balmer series do not overlap. Verify this statement by calculating the longest wavelength associated with the Lyman series and the shortest wavelength associated with the Balmer series. 10. You measure the wavelength of the emission maximum from a small pinhole in an electrically heated container (i.e. a ‘blackbody’) at a series of temperatures and obtain the results given below. Use these results to deduce a value for Planck’s constant. T (°C): 1000 1500 2000 2500 3000 3500 ?max (nm): 2181 1600 1240 1035 878 763

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