An αparticle (^1 He nucleus) is to be taken apart in the...

An $\alpha$ particle ($^{1} \mathrm{He}$ nucleus) is to be taken apart in the following steps. Give the energy (work) required for each step: (a) re- move a proton, (b) remove a neutron, and (c) separate the remaining proton and neutron. For an $\alpha$ particle, what are (d) the total binding energy and (e) the binding energy per nucleon? (f) Does either match an answer to $(a),(b),$ or $(c) ?$ Here are some atomic $$\begin{array}{lllll}{^{4} \mathrm{He}} & {4.00260 \mathrm{u}} & {^{2} \mathrm{H}} & {2.01410 \mathrm{u}} \\ {^{3} \mathrm{H}} & {3.01605 \mathrm{u}} & {^{1} \mathrm{H}} & {1.00783 \mathrm{u}} \\ {\mathrm{n}} & {1.00867 \mathrm{u}}\end{array}$$

An $\alpha$ particle ($^{1} \mathrm{He}$ nucleus) is to be taken apart in the following steps. Give the energy (work) required for each step: (a) re-
move a proton, (b) remove a neutron, and (c) separate the remaining proton and neutron. For an $\alpha$ particle, what are (d) the total
binding energy and (e) the binding energy per nucleon? (f) Does either match an answer to $(a),(b),$ or $(c) ?$ Here are some atomic
$$\begin{array}{lllll}{^{4} \mathrm{He}} & {4.00260 \mathrm{u}} & {^{2} \mathrm{H}} & {2.01410 \mathrm{u}} \\ {^{3} \mathrm{H}} & {3.01605 \mathrm{u}} & {^{1} \mathrm{H}} & {1.00783 \mathrm{u}} \\ {\mathrm{n}} & {1.00867 \mathrm{u}}\end{array}$$

Key Concepts

Mass Defect

Mass defect refers to the difference between the mass of a fully assembled nucleus and the sum of the masses of its individual nucleons. This difference, due to the conversion of mass into binding energy during nuclear formation, is a key quantity that allows one to calculate the binding energy using mass?energy equivalence.

Nuclear Binding Energy

Nuclear binding energy is the energy required to disassemble a nucleus into its individual protons and neutrons. It reflects the energy released when a nucleus is formed from these nucleons and, conversely, the energy needed to break it apart. This concept is central to understanding the stability of nuclei and the energetics of nuclear reactions.

Mass-Energy Equivalence

Mass-energy equivalence, encapsulated by Einstein's formula E=mc², is the principle that mass can be converted into energy and vice versa. In nuclear physics, this relationship is crucial because it explains how small differences in mass (the mass defect) can correspond to large amounts of energy, such as the binding energy holding a nucleus together.

Nuclear Separation Energy

Nuclear separation energy is the specific amount of energy required to remove one nucleon (a proton or a neutron) from a nucleus. It provides a measure of how tightly a nucleon is bound within the nucleus and is used to assess the stability of the nucleus with respect to different types of particle emissions.

Atomic Mass Unit (u)

The atomic mass unit is a standardized unit of mass that quantifies the mass of atoms and subatomic particles. It is defined relative to the mass of a carbon-12 atom and is used in nuclear physics to measure the small mass differences between nuclei and their constituent particles, which are essential in calculating the energy changes in nuclear reactions.

Transcript

00:01 42 .22, we want to take an alpha particle apart, maybe with some very small pleasers or something.

00:11 And so we want to find the amount of work to do each of these steps and then talk about the binding energy of the entire alpha particle and pernucleon and then compare whether that corresponds to any of the steps needed to disassemble the alpha particle.

00:36 Now the first step we want to remove a proton so we can write this as we want to take our helium four and turn it into a proton which in order to have the electrons behave themselves.

00:59 We would write as a helium one atom, hydrogen, hydrogen one atom and then a hydrogen three atom because this will have one proton left and then two neutrons and we're conveniently given the masses of all of these things.

01:24 So it's sort of a hint that this is the right idea.

01:31 So let's call the energy for this delta e1.

01:40 So this is going to be the mass of the hydrogen three plus the mass of the hydrogen one minus the mass of the helium four times c squared because it's an energy.

02:13 And so this is sort of the final energy minus the initial energy.

02:17 So that would be the change.

02:22 And this is 19 .8 mega electron volts.

02:31 It's positive because we had to do work on the nucleus to take the proton out.

02:41 If this were negative, then alpha particles wouldn't be stable.

02:45 They wouldn't find them everywhere.

02:56 Part b, we want to remove a neutron, which we can write as taking our hydrogen three atom, is probably quite unhappy about existing.

03:12 Actually, i don't think hydrogen 3 is that radioactive, but nevertheless, and we get ourselves a neutron plus a hydrogen 2 atom.

03:30 Here we'll call this delta e2 because it's our second step.

03:36 And this is basically rinsing and repeating what we did before, except the masses we're using are different.

03:48 But conceptually, it's a different.

03:50 Exactly the same thing...

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