Answer to Question #118606 in Atomic and Nuclear Physics for Harriet

Question

What is the wavelength of the photon emitted by a hydrogen atom when a bound electron in the n = 3 state makes the transition to the n = 2 state? (to 2 s.f in nm)

Answer 1

We may use the Rydberg formula (https://en.wikipedia.org/wiki/Rydberg_formula):

$\dfrac1\lambda = R\left( \dfrac{1}{n_1^2}-\dfrac{1}{n_2^2}\right).$ Here $R\approx 1.097\cdot 10^7 \,\mathrm{m}^{-1}.$

In our case $n_1 =2, \, n_2 = 3.$ Therefore,

$\dfrac1\lambda = 1.097\cdot10^7\left( \dfrac{1}{2^2}-\dfrac{1}{3^2}\right) \Rightarrow \lambda = 6.563\cdot10^{-7}\,\mathrm{m} = 656.3\,\mathrm{nm}.$

Such a line is called Balmer-$\alpha$ or $\mathrm{H}_{\alpha}.$