Question

A proton and an electron, both at rest initially, combine to form a hydrogen atom in the ground state. A single photon is emitted in this process. What is its wavelength?

Answer 1

The wavelength is

$$\lambda=\frac{hc}E=\frac{hc}{\Delta mc^2}=\frac{h}{\Delta mc}=67.9\text{ pm}.$$

In this equation:

$$\Delta m=m_\text{H}-(m_p+m_e).$$