Physics: Proving Neutrons Exist (or Why Chadwick Got his Nobel Prize) (1/9)

Back in the 30s, the Joliot-Curies discovered a very high-energy radiation from polonium-emitted alpha particles to beryllium. The radiation shot out protons in a proton-heavy substance, parrafin wax, and so they suspected it was a high energy photon. Chadwick calculated the photon would have 52 MeV or so. Verify that.

Eg1 + Ep1 = Eg2 + Ep2
Eg1 + mp = Eg2 + mp + KEp By E = m + KE
Eg1 = Eg2 + KEp
Eg1 = Eg2 + (mp)(γ- 1)

pg1 = pg2 + pc
pg1 + (-pg2) = pc
Eg1 + Eg2 = pc By E^2 = p^2 for photons
Eg1 + Eg2 = (mp)(v)(γ) by the definition for momentum

Eg1 = [(mp)(v)(γ) - Eg1] + (mp)(γ- 1)
Eg1 = (mp/2)[γ(v + 1) - 1 ]
Eg1 = 52.67 MeV , by my plugging in, based on given data

A photon with such energy would cause a 410 KeV recoil in nitrogen. Show it.

Eg1 + EN1 = Eg2 + EN2
(Eg1) + mN = Eg2 + mN + KEN
KEN = (Eg1) - Eg2

pg1 = pg2 + pN2
pg2 = pN2 + (-pg1)
Eg2 = pN2 - (Eg1)

KEN = (Eg1) - [pN2 - (Eg1)]
KEN = pN2 - (2Eg1)
KEN - (2Eg1) = ((EN2)^2 - (mN2)^2 )^-1/2
(KEN)^2 + [4(Eg1)^2] - 2(2Eg1)(KEN) = (mN2)^2 + (KEN)^2 + 2(KEN)(mN2) - (mN2)^2
[4(Eg1)^2] - 2(2Eg1)(KEN) = 2(KEN)(mN2)
2(KEN)(mN2) + 2(2Eg1)(KEN) = [4(Eg1)^2]
2KEN[mN2 + (2Eg1) ] = [4(Eg1)^2]
KEN = [2(Eg1)^2]/[mN2 + (2Eg1)]

The right side is all constants, and Eg1 = 52 MeV gets me about .41 MeV.