Collision of alpha with Be -> C + gamma

[Elvis 123456789]

Homework Statement

Before the discovery of the neutron, it was proposed that the penetrating radiation produced when beryllium was bombarded with alpha particles consisted of high-energy &gamma rays (up to 50 MeV) produced in reactions such as α + 9Be --> 13C + γ

a.) Calculate the Q value for this reaction.

b.) If 5-MeV alpha particles are incident on 9Be, calculate the energy of the 13C nucleus and, hence, determine the energy of gamma radiation assuming it is emitted as a single photon. Hint: You may neglect the momentum of the γ ray relative to the ¹³C nucleus. Masses: m(⁴He) = 4.0026u, m(⁹Be) = 9.0122u, m(¹³C) = 13.0034u

Homework Equations

m(Z, N) = A*1u +Δ where the Δ stands for the mass excess and A = Z + N

Q = (m_c + m_d - m_a - m_b)c²

The Attempt at a Solution

My main gripe with this problem is that i don't understand why we can neglect the momentum of the gamma ray when conserving momentum. I did the problem with the assumption but can the problem still be done without it?

 

[mfb]

I did the problem with the assumption but can the problem still be done without it?

Sure, it just makes the calculation a bit more complex, and it leads to the same answer within the precision you can achieve with the given mass numbers as the assumption is a very good approximation.