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.

 

[quantumdude]

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]

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?

[?]

 

[quantumdude]

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 m_pc²+K_P, and the total energy of the Al nucleus is m_Alc². You were given K_p, and you'll have to look up m_Al.

After Collision
The total energy of the Si nucleus is m_Sic² (remember they said you could ignore its motion). The total energy of the neutron is m_nc²+K_n. 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 (K_n) you should be able to solve this in short order.

 

[frankR]

I got it.

k_n = (m_p - m_Si - m_n + m_Al)*931.5MeV/amu + k_p = 1.004MeV

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