The inverse square law in electrostatic is $\left|\mathrm{F}\right|=\frac{{e}^{2}}{\left(4{\mathrm{\pi \epsilon }}_{0}\right){r}^{2}}$ for the force between an electron and a proton. The $\left(\frac{1}{r}\right)$ dependence of $\left|\mathrm{F}\right|$ 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, the force would be modified to $\left|\mathrm{F}\right|=\frac{{e}^{2}}{\left(4{\mathrm{\pi \epsilon }}_{0}\right)r}\left[\frac{1}{{r}^{2}}+\frac{\mathrm{\lambda }}{r}\right]·\mathrm{exp}\left(-\mathrm{\lambda }r\right)$ where  and . Estimate the change in the ground state energy of a H-atom if mp were 10-6 times the mass of an electron.

Hint: The electrostatic force provides the required centripetal force.
Step 1: Find the wavelength.
For  the mass of an electron, the energy associated with it is given by-
The wavelength associated with it is given by:
Step 2: Find the potential energy.