Estimate of Atomic Decay Rate

We have the formula

$$\bgroup\color{black} \Gamma_{tot}={e^2(E_i-E_n)\over 2\pi\hba... ...)}\hat{\epsilon}\cdot\vec{p_e}\vert\phi_i\rangle\vert^2 \egroup$$

Lets make some approximations.

$$\begin{eqnarray*} \hat{\epsilon}\cdot\vec{p}&\approx& \vert p\vert=m\vert v\vert... ... {\mathrm F/cm}) \approx 2\times 10^{10} {\mathrm sec}^{-1} \\ \end{eqnarray*}$$

This gives a life time of about 50 psec.