# Photon collision with neutron

I am to calculate everything in a non-relativistic state:

a 15MeV photon is completely absorbed in colliding with a neutron initially at rest. Determine the speed of the neutron:

conservation of momentum:

$$E=\frac{hc}{\lambda}$$
$$15MeV=\frac{1240MeV nm}{\lambda}$$
$$\lambda=8.2667x10^{-5}nm$$

$$p_{photon}=\frac{h}{\lambda}=m_{neutron}v_{post collision}$$
where m is the mass of the neutron and v is its velocity
$$v= \frac{h}{ (8.2667x10^{-5}nm )(1.674927 x10^{-27} kg)}$$
$$v=4785505.59 m/s$$

after collisions, the neutron slows down and comes to rest, it emits a photon using up all the energy stored internally, what is the wavelength of this photon?

$$KE=.5mv^2$$
$$KE=.5(1.674927 x 10^{-27}kg)(4785505.59 m/s)^2$$
$$KE=0.11MeV$$

this is the kinetic energy of the neutron, I was going to subtract that number from 15MeV to get the potential energy and then find the wavelength of the photon using E=hc/lambda, but I think I have already made a mistake somewhere since the KE should be a lot bigger.

I've checked my work several times and I dont know where i went wrong.

also, how do i know how much energy converts to KE and how much converts to PE?

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Astronuc
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