The inverse square law in electrostatics is
Question:

The inverse square law in electrostatics is

$|F|=\frac{e^{2}}{\left(4 \pi \epsilon_{0}\right)} r^{2}$ for the force between an electron and a proton. The $1 \mathrm{r}$ dependence of $|\mathrm{F}|$ can be

understood in quantum theory as being due to the fact that the ‘particle’ of light (photon) is massless. If photons had a mass mp, force would be modified to

$|F|=\frac{e^{2}}{\left(4 \pi \epsilon_{0}\right)} r^{2}\left[\frac{1}{r^{2}}+\frac{\lambda}{r}\right]$ where $\lambda=\mathrm{m} \mathrm{cp} / \hbar$ and $h=h / 2 \pi$. Estimate the change in the ground

state energy of an H-atom if mp were 10–6 times the mass of an electron.

Solution:

Mass of photon = 9.1 × 10-37 kg

Wavelength associated with the photon = h/mpc

Total energy E = -13.6 + 27.2 λ rA

Where λrA = δ