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1 PRACTICE PROBLEMS FOR 2 nd HOUR-TEST, 20A-1, FALL 07 1. Suppose we shine light of a certain frequency on a hydrogen atom whose electron is in its next-to-lowest (n=2) energy state and we observe that the electron is ejected with a kinetic energy of 3.0 ev. What was the frequency of the light? SOLUTION: The electron in n=2 has energy –I/4, where I = 2.18 x 10 -18 J. Thus it must be given an energy of +I/4 to be freed from the nucleus with no excess (kinetic) energy, i.e., have a total energy of zero; but the incident light has more energy than this by 3.0 ev, implying h ν = 3.0 ev (1.6 x 10 -19 J /ev) + (2.18 x 10 -18 J)/4, from which you can solve for the frequency ν . 2. Now consider a different hydrogen atom, whose electron is excited to one of the n=4 states. What are the emission frequencies you should expect to observe as this atom undergoes transitions to lower energy states? SOLUTION: The atoms will undergo transitions from n=4 to n=3, to n=2 and to n=1, with corresponding frequencies (E 4 -E 3 )/h, (E 4 -E 2 )/h, and (E 4 -E 1 )/h. But when n=3 states are formed by the first of these transitions, they can in turn undergo transitions to n=2 and to n=1, and similarly n=2 can undergo a transition to n=1. So there is a total of six emission frequencies that can be observed.
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