Solution

Solution

The Energy for the hydrogen atom is described by:

$E={\frac {P^{2}}{2m}}-{\frac {e^{2}}{r}}$

$\Delta r$ is defined as the average radius of localization for the electron. Appropriately, the uncertainty principle can be generalized as:

$\Delta r\cdot \Delta p\backsimeq \hbar$

Thus the momentum corresponding to $\Delta r$ and the corresponding kinetic energy are usefully defined as:

$p\backsimeq \Delta p\backsimeq {\frac {\hbar }{\Delta r}}$

$KE={\frac {P^{2}}{2m}}\backsimeq {\frac {\hbar ^{2}}{2m(\Delta r)^{2}}}$