The Structure of the Atom: example

What wavelength of light is emitted by an electron dropping from the third orbital to the ground state of a hydrogen atom?

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Strategy
The ground state of a hydrogen atom is considered the first orbital of the atom. As a result, n_f = 1 and n_i = 3. The Rydberg constant has already been determined and will be constant regardless of atom chosen.
Solution
$\frac{1}{λ} = R (\frac{1}{n_{f}^{2}} - \frac{1}{n_{i}^{2}})$
22.29

For the equation above, calculate wavelength based on the known energy states.

$\frac{1}{λ} = 1.097 \times 10^{7} (\frac{1}{1^{2}} - \frac{1}{3^{2}}) = 9.751 \times 10^{6} m^{−1}$
22.30

Rearranging the equation for wavelength yields

$λ = 1.026 \times 10^{−7} m = 102.6 nm .$
22.31

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