# Homework Help: Determining Neutron Wavelength with mass alone

1. Sep 26, 2011

### atomicpedals

1. The problem statement, all variables and given/known data

Consider a particle of mass m in the potential

V(z)=mgz z>0, infinity if z<0

Show that the wavelength of a neutron (m~1000MeV/c^2) is on the order of 10um.

2. Relevant equations

p=(2m(E-mgz))1/2
$\lambda$=h/p

3. The attempt at a solution

The most direct solution would seem to simply be

h/(2m(E-mgz))1/2 (with appropriate substitutions)

however, that still leaves the factors of g and z to be resolved... I could take z as 1, but there's still g with a units problem (m/s/s vs MeV and MeV/c^2).

Any suggestions?

2. Sep 27, 2011

### vela

Staff Emeritus
Try drawing a diagram of the potential and then sketch what the ground-state wave function will look like. That should give you an idea for a relationship between the wavelength and the energy of the neutron.

3. Sep 27, 2011

### atomicpedals

So, for z>0 the potential will increase linearly (holding m and g constant).