For the hydrogen atom, the energy of the n^{th} state is:

$\overline{)\begin{array}{rcl}{\mathbf{E}}_{\mathbf{n}}& {\mathbf{=}}& \frac{\mathbf{13}\mathbf{.}\mathbf{6}}{{\mathbf{n}}^{\mathbf{2}}}\mathbf{e}\mathbf{V}\end{array}}$

Energy and wavelength are related by:

$\overline{)\begin{array}{rcl}{\mathbf{E}}& {\mathbf{=}}& \frac{\mathbf{h}\mathbf{c}}{\mathbf{\lambda}}\end{array}}$

**(a) **

Emission occurs when an electron moves from n_{i} to n_{f} such that n_{f} is less than n_{i}.

For n = 5, the transitions are: 5→1, 5→2, 5→3, 5→4 (4 wavelengths)

Electrons falling in n = 4, n = 3, and n = 2 will also give the following transitions as they fall to ground state (n = 1).

A monochromatic laser is exciting hydrogen atoms from the n = 2 state to the n = 5 state. Eventually, all of the excited hydrogen atoms will emit photons until they fall back to the ground state.

(a) How many different wavelengths can be observed in this process?

(b) What is the shortest wavelength λ_{min} observed?

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