As part of his discovery of the neutron in 1932, James Chadwick determined the mass of the neutron (newly identified particle) by firing a beam of fast meutrons, all having the same speed, as two different targets and measuing the maximum recoil speeds of the target nuclei. The maximum speed arise when an elastic head-on collision occurs between a neutron and a stationary target nucleus. Represent the masses and final speeds of the two target nuclei as `m_(1), v_(1), m_(2)` and `v_(2)` and assume Newtonian mechanics applies. The neutron mass can be calculated from the equation:
`m_(n) = (m_(1)v_(1) - m_(2)v_(2))/(v_(2) - v_(1))`
Chadwick directed a beam of neutrons on paraffin, which contains hydrogen. The maximum speed of the protons ejected was found to be `3.3 xx 10^(7) m//s`. A second experiment was performed using neutrons from the same source and nitrogen nuclei as the target. The maximum recoil speed of the nitrogen nuclei was found to be `4.7 xx 10^(6) m//s`. The masses of a proton and a nitrogen nucleus were taken as `1u` and `14 u`, respectively. What was Chadwick's value for the neutron mass?

Options

A. `1.16 u`
B. `1.47 u`
C. `0.95 u`
D. `1.80 u`

Answer

A

Explanation

`m_(n) = (m_(1)v_(1) - m_(2)v_(2))/(v_(2) - v_(1))`
`= (14 xx (4.7 xx 10^(6)) - 1xx (3.3 xx 10^(7)))/(3.3 xx 10^(7) - 4.7 xx 10^(6)) = 1.16`