How Long Does an Electron Stay in the Hydrogen 2p State?

[thesage]

The problem statement
An electron going from 2p to 1s state in hydrogen sits up at the 2p for a while then jumps down.
with the given eqn
W=\frac {4*\alpha*\omega^3}{3*c^2}*\mid r12\mid^2
\mid r12\mid^2=\mid<1\mid x\mid2>\mid^2+\mid<1\mid y\mid2>\mid^2+\mid<1\mid z\mid2>\mid^2

alpha is fine structure cons, omega is the energy diff and c is speed of light

I'd imagine the life time is 1/W as the rate is per second.

The attempt at a solution
The question is okay except for the \mid r12\mid^2 part. Is the \mid r12\mid^2 part the expectation value of r or do i need to do the x,y,z separatly. The statement, in the question, of what \mid r12\mid^2 is confuses me.

 

[andresordonez]

You have to do it separately, the expectation value is the matrix element of an operator between the same states, here you have two different states.