The Sudden Approximation: Examining Perturbations on Atomic Electron Motion

[bon]

Homework Statement

In the beta decay of tritium (1 proton, 2 neutron) to helium, the emitted electron has a kinetic energy of 19keV. We will consider the effects on the motion of the the atomic electron (the one orbiting the nucles) which we assume is initially in the ground state of tritium.

(a) show that the perturbation is sudden by considering the location of the emmitted electron at a time around T = 5x10^-7 s after emission. How does T compare with the time scale on which the wavefunciton changes.

Homework Equations

The Attempt at a Solution

Well I've worked out the electron would have traveled 3.75 x 10^-9 m. And i know the time scale the wavefn changes is hbar/E but which E do i use? the one for the atomic electron or the other electron? What is this meant to show?

Thanks

 

[bon]

anyone?

 

[ideasrule]

You're trying to see whether the perturbation on the atomic electron, by the emitted electron, is sudden. To do this, the question gives a time T by which the emitted electron would be very far from the nucleus. You're trying to compare T with the timescale on which the atomic electron's wavefunction changes, so it only makes sense to use the atomic electron's E.