Module 6: C26 - Nuclear Physics

Question 1

What is the Rest Mass on an object

Answer 1

The mass of an object, such as a particle, when it is stationary

Question 2

What are the two interpretations of Einstein’s Mass-Energy equation E = mc^2

Answer 2

• Mass is a form of energy
• Energy has mass

Question 3

What is the first interpretation of E = mc^2

Answer 3

The first interpretation is that mass is a form of energy.

The interaction of an electron-positron pair illustrates this idea well - the particles completely destroy each other (annihilation) and the entire mass of the parties is transformed into two gamma photons.

Question 4

What is the second interpretation of E = mc^2

Answer 4

The second interpretation is that energy has mass.

The change of mass of an object, or a system, is related to the change in its energy, shown by ΔE = Δmc^2

A moving ball has kinetic energy, implying that its mass is greater than its rest mass. Similarly a decrease in the energy of system means the mass of the system must also decrease, like the mass of mug of hot tea will decrease as it cools and loses thermal energy.

Question 5

Example Question:

Consider a person with rest mass 70 Kg sitting in a stationary car. Now imagine the car travelling at a steady speed of 15 ms-1. The person has gained kinetic energy, an increase in energy. The person will therefore have increased mass.

Calculate the change in mass.

Answer 5

ΔE = Δmc^2
Δm = ΔE/c^2
Δm = (1/2mv^2) / c^2

Δm = (1/2 x 70 x 15^2) / (3x10^8)^2
Δm = 8.8x10^-14 kg

Question 6

In natural radioactive decay, why is the mass of the daughter nucleus and alpha particle less than the original parent nucleus.

Answer 6

As energy is released in radioactive decay, a decrease in mass has to take place too.

This means the total mass of the alpha particle and daughter nucleus must be less than the mass of the parent nucleus.

This decrease in mass Δm is equivalent to the energy released ΔE

Question 7

Example Question:

Positrons are the antiparticles of electrons. When they meet, they annihilate each other, and their entire mass is transformed into energy in the form of two identical gamma photons. Calculate the minimum energy of each photon.

Answer 7

Mass of electron/positron = 9.11x10^-31

E = mc^2
E = [(2 x 9.11x10^-31) x (3x10^8)^2] / 2 = 8.199x10^-14

Question 8

What is Pair Production

Answer 8

Pair production is the replacement of a single
photon with a particle and a corresponding
antiparticle of the same total energy.

Question 9

When two protons collide is the total rest mass higher before or after the collision

p + p —> p + n + π^+

Answer 9

The total rest mass of the particles after the collision is greater than before. The increase Δm multiplied by c^2 must be equal to the minimum kinetic energy of the colliding protons.

Question 10

Example Question:

Mass of a deuterium nucleus = 2.013553 u
Mass of proton = 1.007276 u
Mass of neutron = 1.008665 u
Mass of electron = 0.00055 u

a) What is difference between a mass of a deuterium and separated proton and neutron.

b) Calculate the energy equivalent of a deuterium nucleus.

c) Calculate the total energy equivalent of a proton and a neutron.

Answer 10

a)
Sum of parts : 2.016491 u
Mass: 2.013553 u

Difference: 2.388x10^-3 u

b)
E = mc^2
2.01355 x 1.661x10^-27 = 3.345x10^-27
E = (3.345x10^-27) x (3x10^8)^2
E = 3.01006x10^-10 J

c)
1.007276u + 1.008665u = 2. 015941u
2.015941 x 1.661x10^-27 = 3.348x10^-27
3.348x10^-27 x (3x10^8)^2 = 3.01363021x10^-10 J

Question 11

What is Mass Defect

Answer 11

The mass defect of a nucleus is defined as the difference between the mass of the completely separated nucleons and the mass of the nucleus.

Question 12

What is Binding Energy

Answer 12

The binding energy is the minimum energy required to completely separate a nucleus into its constituent protons and neutrons.

Question 13

What is the Binding Energy per nucleon

Answer 13

Binding energy per nucleon is a more useful quantity as it compares the binding energy to the number of nucleons in an atom.

Question 14

The mass of a uranium-235 (nucleon number: 235, proton number:92) nucleus is 235.004393u.

Calculate its binding energy in MeV.

Answer 14

Step 1: Calculate the total mass of the constituent nucelons.

The uranium-235 nucleus has 92 protons and (235-92) = 143 neutrons.

Therefore, mass of nucleons = (92x1.007276) + (143 x 1.008665) = 236.908487 u

Step 2: Calculate the mass defect for the uranium-235 nucleus.

Mass defect = 235.004393 - 236.908487 = (-)1.904094u

Step 3: Change the mass defect from u to kg
(1u = 1.661x10^-27 kg)

Mass defect = 1.904094 x 1.661x10^-27 = 3.162x10^-27 kg.

Step 4: Calculate the binding energy and convert it from J to eV using the conversion factor 1eV = 1.60x10^-19 J

Binding energy = mass defect x c^2
Binding energy = 3.162x10^-27 x (3.0x10^8)^2 = 2.84x10^-10 J
Binding energy = 2.84x10^-10 / 1.60x10^-19 = 1.779x10^9 eV
Binding energy = 1780 MeV

Question 15

What does the binding energy per nucleon say about how stable the nucleus is

Answer 15

The greater the binding energy (BE) per nucleon, the more tightly bound the nucleons within the nucleus are, or in the other words a nucleus is more stable if it has greater BE per nucleon.

Question 16

What element nucleus has the greatest (Binding Energy) per nucleon?

Answer 16

The nucleus of iron-56 (Fe) has the greatest BE per nucleon - it is the most stable isotope in nature

Question 17

What is Induced Fission

Answer 17

Nuclear fission occurring when a nucleus becomes unstable on absorbing another particle (such as a neutron)

Question 18

What is a thermal neutron

Answer 18

A neutron in a fission reactor with mean kinetic energy similar to the thermal energy of particles in the reactor core - also known as a slow neutron.

Question 19

What is a typical induced fission reaction of uranium-235 by a thermal neutron

Answer 19

¹₀n + ²³⁵₉₂U —> ²³⁶₉₂U —> ¹⁴¹₅₆Ba + ⁹²₃₆Kr + 3 ¹₀n

Question 20

Describe the process of a typical induced fission reaction of uranium-235 by a thermal neutron

Answer 20

The uranium-235 nucleus captures a thermal neutron and becomes a highly unstable nucleus or uranium-236. In less than a microsecond, the uranium-236 nucleus splits. The daughter nuclei produced in this example are barium-141 and krypton-92. Three fast neutrons are also produced. The equation is balanced as the number of protons and nucleons are conserved

Question 21

How is energy emitted from nuclear fission

Answer 21

The total binding energy of the particles after fission is greater than the total binding energy before it. The difference in binding energies is equal to the energy released.

The energy released in a single fission reaction is a combination of kinetic energy if the particles produced and the energy of photons and neutrinos emitted.

Question 22

Explain how nuclear fission can provide energy

Answer 22

It can provide energy, as the uranium becomes unstable with the extra neutron and will split up into two other elements and fast neutrons. Energy is also produced in this reaction, as the mass of the system decreases (E=mc^2)

Question 23

Worked example: Energy from fission
The difference in mass in the induced fission of uranium-235 is about 0.185u.

Calculate the total energy released in this reaction in MeV.

Answer 23

Step 1: Change Δm from u to kg (1u = 1.661x10^-27kg).

Δm = 0.185 x 1.661x10^-27 = 3.07x10^-28 kg

Step 2: Use Einstein’s mass-energy equation to calculate the energy released

Energy released ΔE = mc^2
ΔE = 3.07x10^-28 x (3.00x10^8)^2 = 2.76x10^-11J

Step 3: Change the energy from joules to electron volts

(1eV = 1.60x10^-19J)
ΔE = 2.76x10^-11/1.6x10^-19 = 172.5x10^6 eV = 170MeV

Question 24

What might happen if the three fast neutrons produced in a fission reaction are slowed down

Answer 24

A chain reaction becomes possible, with these three neutrons starting three more reactions, which each produce another three neutrons, and so on.

Question 25

How is the steady production of power ensured in a nuclear reactor

Answer 25

The steady production of power from a nuclear reactor is controlled by ensuring that, on average, one slow neutron survives between successive fission reactions.

Question 26

What is the setup inside a fission reactor

Answer 26

Fuel rods are spaced evenly within a steel-concrete vessel known as the reactor core. A coolant is used to remove the thermal energy produced from the fission reactions within the fissile fuel. The fuel rods are surrounded by the moderator, and control rods can be moved in and out.

Question 27

What are the Fuel Rods and what is its job

Answer 27

Fuel rods contain enriched uranium, which consists mainly of uranium-238 with 2-3% uranium-235.

Question 28

What is the Moderator and what is its job

Answer 28

The role of the moderator is to slow down the fast neutrons produced in fission reactions. The material for a moderator must be cheap and readily available, and must not absorb the neutrons in the reactor.

Fast-moving neutrons just bounce off the massive uranium nuclei with negligible loss of kinetic energy. However, when they collide Elastically with protons (or deuterium) in water or with carbon nuclei, they transfer significant kinetic energy and slow down. Water and carbon are therefore good candidates for a moderator.

Question 29

What are the Control Rods and what is its job

Answer 29

The control rods are made of a material whose nuclei readily absorb neutrons, most commonly boron or cadmium. The position of the control is automatically adjusted to ensure that exactly one slow neutron survives per fission reaction. To slow down or completely stop the fission, the rods are pushed further into the reactor core.

Question 30

What is a dangerous by product of nuclear fission of uranium

Answer 30

Plutonium-239 is one of the most hazardous materials produced in nuclear reactors. It is extremely toxic as well as radioactive, and it has a half-life of 24 thousand years. The daughter nuclei produced from its numerous fission reactions are also radioactive.

Question 31

Downsides of Nuclear Power production

Answer 31

Radioactive waste from nuclear reactors cannot be disposed of as normal waste. The storage of radioactive waste presents us with both practical and ethical issues. High-level radioactive waste, which includes spent fuel rods, has to be buried deep underground for many centuries because isotopes with long half-lives must not enter any water or food supplies

Question 32

What conditions are needed for two nuclei to undergo a fusion reaction

Answer 32

• Bring them close together, 10^-15m so that the shirt-range nuclear force can attract them into a larger nucleus.
• All nuclei have a positive charge, so they will repel each other. The repulsive electrostatic force between nuclei is enormous at small separations
• At low temperatures, the nuclei cannot get close enough to trigger fusion
• At higher temperatures, they move faster and can get close enough to absorb each other through the strong nuclear force.

Question 33

Why does do fusion reactions occur in the sun (what conditions do the sun have)

Answer 33

Temperature is close to 1.4x10^7K and the density is 1.5x10^5 kgm^-3. The enormous density ensures a higher number of fusion reactions per second.

Question 34

Example of a fusion cycle, starting with 2 protons

Answer 34

• Two protons fuse together to produce a deuterium nucleus (²₁H), a positron, and neutrino. This reaction produces about 2.2 MeV of energy

¹₁p + ¹₁p —> ²₁H + ⁰+₁e + v

• The deuterium nucleus from the first reaction fuses with a proton. A helium-3 nucleus is formed and 5.5MeV of energy is released

²₁H + ¹₁p —> ³₂He

• The helium-3 from the second reaction combines with another helium-3 nucleus. A helium-4 nucleus is formed, together with two protons, and 12.9MeV of energy

³₂He + ³₂He —> ⁴₂He + 2 ¹₁p

• The whole cycle is repeated again with the two protons. This cycle is known as the proton-proton cycle, or the hydrogen-burning cycle

Question 35

What is the main problem with Fusion Power Plants

Answer 35

The main problems centre on maintaining high temperatures for long enough to sustain fusion, and on finding the extremely hot fuel within a reactor.