# Problem: 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 λmin observed?

###### FREE Expert Solution

For the hydrogen atom, the energy of the nth 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 ni to nf such that nf is less than ni.

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).

###### Problem Details

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 λmin observed?