As part of his discovery of the neutron in 1932 , James...

As part of his discovery of the neutron in 1932 , James Chadvick determined the mass of the newly identified particle by firing a beam of fast neutrons, all having the same speed, at two different targets and measuring the maximum recoil speeds of the target nuclei. The mum speeds arise when an elastic head-on collision occurs between a neutron and a stationary target nucleus. (a) 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 applics. Show that the neutron mass can becalculated from the cquation $$ m_{n}=\frac{m_{1} v_{1}-m_{2} v_{2}}{v_{2}-v_{1}} $$ (b) Chadwick directed a beam of neutrons (produced from a nuclear reaction) on parafin, which contains hydrogen. The maximum speed of the protons ejected was found to be $3.3 \times 10^{7} \mathrm{m} / \mathrm{s}$ . Because the velocity of the neutrons could not be determined directly, 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 $4.7 \times 10^{6} \mathrm{m} / \mathrm{s}$ . The masses of a proton and a nitrogen nucleus were taken as 1 $\mathrm{u}$ and 14 $\mathrm{u}$ , respectively. What was Chadwick's value for the neutron mass?

As part of his discovery of the neutron in 1932 , James Chadvick determined the mass of the newly identified particle by firing a beam of fast neutrons, all having the same speed, at two different targets and measuring the maximum recoil speeds of the target nuclei. The mum speeds arise when an elastic head-on collision occurs between a neutron and a stationary target nucleus. (a) 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 applics. Show that the neutron mass can becalculated from the cquation
$$
m_{n}=\frac{m_{1} v_{1}-m_{2} v_{2}}{v_{2}-v_{1}}
$$
(b) Chadwick directed a beam of neutrons (produced from a nuclear reaction) on parafin, which contains hydrogen. The maximum speed of the protons ejected was found to be $3.3 \times 10^{7} \mathrm{m} / \mathrm{s}$ . Because the velocity of the neutrons could not be determined directly, 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 $4.7 \times 10^{6} \mathrm{m} / \mathrm{s}$ . The masses of a proton and a nitrogen nucleus were taken as 1 $\mathrm{u}$ and 14 $\mathrm{u}$ , respectively. What was Chadwick's value for the neutron mass?

Key Concepts

Newtonian Mechanics

This is the framework that uses the classical equations of motion and is applicable when speeds are much less than the speed of light. In this context, Newtonian mechanics provides the basis for calculating momentum and energy changes during collisions between particles.

Elastic Collisions

An elastic collision is one in which both momentum and kinetic energy are conserved. Understanding elastic collisions allows one to relate the initial and final speeds of particles involved, which is key to deducing properties such as mass from experimental recoils.

Momentum Conservation

Momentum conservation is the principle that the total momentum of a closed system remains constant before and after a collision. This principle is used to relate the masses and velocities of the colliding particles, enabling the calculation of unknown masses in controlled experiments.

Recoil Kinematics

Recoil kinematics involves analyzing the motion of a target particle after it has been struck, particularly its maximum speed in a head-on collision. This concept is critical in experiments where the properties of the incident particle, such as mass, are inferred from the measured recoil speeds.

Transcript

00:01 In this question, we are looking at the elastic collision of a neutron with a stationary target.

00:08 So we have a neutron bombarding a stationary target, nuclei, which we have no idea.

00:17 What is the nuclei? it's an unknown nucleic.

00:21 I want to find the equation relating the mass of the neutron to the final recoil velocity.

00:31 Velocity or the maximum recoil velocity of this of this particle of this nuclei so we know that it undergoes this elastic collision so elastic collision means that the momentum is conserved and also the kinetic energy is conserved so if you are to use the equations for conservation of energy and conservation of momentum.

01:09 You should be able to derive an equation at 9 .24 from chapter 9 .9.

01:17 The kinematic equation would be the final velocity of this particle.

01:28 Let us call this v1 after it has been collided.

01:32 V1 equals to 2 times m n divided by n plus m1 e unknown multiplied by vn vn vn which is the initial velocity of our neutron this is only valid for elastic collisions where the initial velocity of the unknown mass is zero right so this is a stationary at its start now this will apply to both the mass one as well as mass two make two different masses so b2 also will have the same expression since we are given that the velocity of the neutron bombarding both of them is the same now from these two equations of course we can actually simplify them 2mn vn, which is the numerator plus the external factor is equal to we multiply the denominator across.

03:12 We can do the same thing for the first equation as well, which is right.

03:37 From here, we can actually solve for mn.

03:43 By rearranging and opening up the brackets...

Please give Ace some feedback