Kinetic Engergy in a Quantum Oscillator

[cowmoo32]

How much kinetic engergy in eV must an election beam have to be able to excite a quantum oscillator from its ground state to two levels above the ground state if the mass is 3e-26kg and the spring stiffness is 80N/m?

All I can find is the spacing between the energy levels, I have no idea how to find K. The answer is 6.8e-2 J, but I don't have a clue how to get there.

 

[dextercioby]

I can only assume that you can convert whatever energy (number) you got to kiloelectronvolts.

Daniel.

 

[cowmoo32]

I got 2.8e61 using the forumla DeltaE = hbar*sqrt(Ks/m)
but this is the space between engergy levels. I don't know how to calculate the kinetic energy of the electron beam.

 

[cowmoo32]

my book has the forumla K + U = (.5p^2/m) + .5Ks^2+U0
but I'm not sure what K would be equal to. Granted, it's obvious it would be (.5p^2/m) + .5Ks^2+U0-U but I don't know U either.

 

[dextercioby]

It means that you don't understand the question: the electron beam's energy is at least equal to the energy the quantum oscillator gets in order to jump from the fundamental level to the second excited one. For simplicity, take it as equal.

Daniel.

 

[cowmoo32]

Ok, the beam has to have as much energy as it takes for the electron to move from one energy level to the next, I understand that. But I still don't understand how to arrive at the answer. The answer I got is nowhere near the correct answer.

 

[dextercioby]

Maybe it's a number/conversion problem. I'm n ot going to show such trivial computation and maybe no one will.

Daniel.