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 neutrons , all having the same speed, as two different targets and measuring the maximum recoil speeds of the target nuclei. The maximum speed arise when an elastic head-on colliion 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 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 ( in u ) ?

Answer

`00001.16`