An α -particle and a free electron, both initially at rest combine to form a H e + ion in its ground state with the emission of a single photon. the energy of the photon is:

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Concept: Hydrogen-like atom ionization energy

The energy of the emitted photon equals the ionization energy of $H e^{+}$ .

$E = 13.6 Z^{2} (\frac{1}{n _{1}^{2}} - \frac{1}{n _{2}^{2}})$ eV,

$13.6 * 2^{2} = 54.4$

where $n_{1} = 1$ and $n_{2} = \infty$

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