Hmwk4 - Chem2070 Homework#4 Fall 2011 Due September 23 1...

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Chem2070 Fall 2011 Homework #4: Due September 23 1. Suppose an atom in an excited state can return to the ground state in two steps. If first falls to an intermediate state emitting radiation of wavelength λ 1 , and then to the ground state, emitting radiation of wavelength λ 2 . The same atom can also return to the ground state in one step, emitting one photon of wavelength λ . How are λ, λ 1 , and λ 2 related? How are their frequencies related (in both cases, write an algebraic expression, not a word explanation). 2. In the Bohr model, the energy of an electron orbital is E n ( Z ) = 1 . 097 × 10 7 m Z 2 n 2 = 1 91 . 16 nm Z 2 n 2 for nuclear charge Z , and the electron orbits the nucleus at a distance r n = n 2 Z a 0 where a 0 = 0 . 053 nm. (a) Without any detailed calculations, indicate which of the following energy transi- tions in He + requires absorption of the most energetic photon. i. from n i = 1 to n f = 2 ii. from n i = 2 to n f = 4 iii. from n i = 3 to n f = 9 iv. from n i = 10 to n f = 1
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