# Determine the kinetic energy of the emerging neutrons

#### frankR

A beam of 6.61MeV protons is incident on a tanget of 2713Al. Those that collide produce the reaction

p + 2713Al ---> 2714Si + n

(2714Si has a mass of 26.986721amu.) Neglect any recoil of the product nucleous and determine the kinetic energy of the emerging neutrons.

Okay, what the heck is the idea here?

I tried conserving the mass and the energy. What am I missing?

The correct answer should be 1.00MeV, I get a number much bigger than that.

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#### Tom Mattson

Staff Emeritus
Gold Member
I tried conserving the mass and the energy. What am I missing?
Without seeing your work, it's hard to tell what you are missing. I remember in another thread you were using nonrelativistic KE in a relativistic particle collision problem. Could that be it?

#### frankR

Re: Re: Nuclear Physics

Originally posted by Tom
Without seeing your work, it's hard to tell what you are missing. I remember in another thread you were using nonrelativistic KE in a relativistic particle collision problem. Could that be it?
Whatever I'm doing is way off the mark, so I didn't want to waste time typing it. I need to know the correct way to attack the problem before I start making calculations.

I started looking at it as a collision:

The protons are moving relativistically, I found their speed to be 3.56*10^7 m/s.

What happens during the collision. I know the Al picks up a proton and becomes Si and a nuetral particle is emitted. I looked the binding energy of Al, it comes out to be a really big number, but how much of that energy gives the n particle KE?

[?]

#### Tom Mattson

Staff Emeritus
Gold Member
Frank,

Don't assume that it's not worth typing out just because your answer is way off. It may be a simple mistake that is easily identified.

Nevertheless...

Before Collision
The total energy of the proton is mpc2+KP, and the total energy of the Al nucleus is mAlc2. You were given Kp, and you'll have to look up mAl.

After Collision
The total energy of the Si nucleus is mSic2 (remember they said you could ignore its motion). The total energy of the neutron is mnc2+Kn. You were given the mass of the Si nucleus and you'll have to look up the mass of the neutron.

Since there is only one unknown here (Kn) you should be able to solve this in short order.

#### frankR

I got it.

kn = (mp - mSi - mn + mAl)*931.5MeV/amu + kp = 1.004MeV

I'm not sure what happened to the nucleon in this collisions/reaction, but I understand the procedure.

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