(9821) Hydrogen decay rate from 2p to 1s

In continuation to Ex.9820, consider the decay of Hydrogen atom from 2p to 1s.

(1) Find the dipole matrix element \( D \) for the transition.

(2) Write the final result for \( \Gamma_0 \) in terms of the \( \alpha = e^2/c \) and the mass \( m_e \) of the electron, incorporting the constants \( c \) and \( \hbar \).