Nuclear And Particle Physics

Question 1

What is radioactive decay?

Answer 1

Radioactive decay is the process in which an unstable atomic nucleus spontaneously loses energy by emitting particles and/or energy and so potentially becomes more stable. It is a random process meaning that it is impossible to predict which of a number of identical nuclei will decay next.

Question 2

State the three types of radiation emitted by radioactive materials, in order from most to least ionising

Answer 2

• alpha particles
• beta particles
• gamma rays

Question 3

State the characteristics of an alpha particle

Answer 3

An α-particle is a helium nucleus consisting of 2p + 2n. It has a mass of 4u, a charge of +2e and can penetrate 2cm of air, skin and paper

Question 4

State the characteristics of a beta particle

Answer 4

A β-particle is a high speed (high energy) electron. It has a mass of 1/2000u (negligible), a charge of -e, and can penetrate a few metres of air, aluminium and perspex

Question 5

State the characteristics of gamma rays

Answer 5

A γ-ray is a high energy photon of electromagnetic radiation. It has no mass, no charge, and can penetrate thick lead and concrete

Question 6

What does a Geiger-Muller tube do, and how does it work?

Answer 6

A Geiger-Muller tube is a device which is used in conjunction with an amplifier and counter (called a scalar) to detect alpha, beta and gamma radiation. It works by detecting ionisation caused by these radiations as they pass through the air

Question 7

Describe Rutherford’s alpha-particle scattering experiment and the results he obtained

Answer 7

Rutherford carried out an experiment where a narrow beam of alpha-particles were fired at thin gold foil (approximately 400 atoms thick) under a vacuum. The deflected alpha-particles were detected on all sides by a ring of scintillators. He observed that:
1. Most of the particles go straight through undeflected
2. A few are deflected through small angles (about 1 in 2000)
3. A very small number are deflected through large angles (about 1 in 10,000)

Question 8

State what was concluded about the atom from Rutherford’s experiment

Answer 8

All the positive charge and most of the mass of the atom are concentrated in the nucleus, diameter 10^-14m rather than an atom’s 10^-10m diameter. In other words, he showed that most of the mass in an atom was in a diameter only a ten thousandth that of a typical atom.

Question 9

Describe the simple nuclear model of the atom

Answer 9

The atom consists of a small, dense, positively charged nucleus surrounded by a cloud of electrons. The nucleus consists of protons and neutrons collectively called nucleons.

Question 10

What are isotopes, and how does their stability vary?

Answer 10

Isotopes are atoms of the same element with the same number of protons but differing numbers of neutrons, which causes the stability of their nuclei to differ greatly

Question 11

What does a nucleon refer to?

Answer 11

A subatomic particle that resides in the nucleus of the atom, either a proton or a neutron.

Question 12

What do atomic (proton) number and mass number represent?

Answer 12

Mass number = number of nucleons in a nucleus (neutrons + protons)
Atomic number = number of protons in a nucleus

Question 13

State the four fundamental forces in order from weakest to strongest

Answer 13

• gravitational force
• weak nuclear force
• electromagnetic force
• strong nuclear force

Question 14

State the properties of the gravitational force

Answer 14

The gravitational force acts on all particles with mass. It is always attractive, has an infinite range and is very weak (relative strength of 10^-40)

Question 15

State the properties of the electromagnetic force

Answer 15

The electromagnetic force acts on static and moving charged particles. It can be both attractive and repulsive, it has an infinite range and has a relative strength of 10^-3.

Question 16

State the properties of the weak nuclear force

Answer 16

The weak nuclear force is the force responsible for beta decay. It acts to change quark types over very small distances (range of 10^-18m) and has a relative strength of 10^-6.

Question 17

State the properties of the strong nuclear force

Answer 17

The strong nuclear force acts between all nucleons and all quarks, and counteracts the repulsive electrostatic forces between protons in the nucleus. It is attractive at small distances up to about 3fm and repulsive at incredibly small distances below about 0.5fm, and has a limited range (about 10^-15m). It has a relative strength of 1.

Question 18

Describe the nature of the strong nuclear force and how it varies with nucleon separation

Answer 18

Within a nucleus, for a typical nucleon separation of 1.3fm, the strong nuclear force is very attractive. Beyond 1.3fm separation, the strong nuclear force quickly reduces to zero. Therefore the strong nuclear force is a very short-range force. When the separation exceeds about 2.5fm the electrostatic force between protons dominates, and they will be propelled apart.

Question 19

What is 1fm in m?

Answer 19

1fm = 10^-15m

Question 20

What is the volume of a nucleus equal to?

Answer 20

V = 4/3πR³, where R is the nuclear radius
Since R = R₀A^1/3
We can also write this as V = 4/3π(R₀A^1/3)³
Or V = 4/3πR₀³A, where A is the mass number

Question 21

State the equation for nuclear radius (R)

Answer 21

R = R₀A^1/3, where R₀ is a constant of proportionality

Question 22

State the equation for mass of a nucleus

Answer 22

m = Au, where A is the mass number and u is the atomic mass unit

Question 23

Derive the equation for nuclear density

Answer 23

ρ = m/V
Since m = Au and V = 4/3πR₀³A
ρ = Au/(4/3πR₀³A)
ρ = 3u/4πR₀³

Question 24

Give four particles (matter) and their corresponding antiparticle (antimatter), and state the symbol for each

Answer 24

Electron (e-) - positron (e+)
Proton (p) - antiproton (pbar)
Neutron (n) - antineutron (nbar)
Neutrino (𝜈) - antineutrino (𝜈bar)

Question 25

State the similarities and differences between matter and antimatter

Answer 25

Antiparticles have the same rest mass as the corresponding particles, but if they are charged, they have equal and opposite charge to the corresponding particle. All other quantum numbers are also opposite.

Question 26

What happens when a particle and its corresponding antiparticle meet at a point in space

Answer 26

They annihilate to produce energy in the form of photons. The rest energy and kinetic energy of the particle and antiparticle is transferred into the energy of the photons

Question 27

Describe the classification of particles

Answer 27

Particles which experience both the strong and weak nuclear force are called HADRONS.
Particles that experience the weak nuclear force but not the strong nuclear force are called LEPTONS.
HADRONS can be split into two groups, BARYONS and MESONS. BARYONS contain the proton in their decay products whereas MESONS do not.

Question 28

Describe the fundamental particle make up of baryons, anti-baryons, mesons and leptons

Answer 28

Baryons are made up of three quarks
Anti-baryons are made up of three antiquarks
Mesons are made up of a quark-antiquark pair
Leptons are themselves fundamental particles, they do not consist of any smaller particles

Question 29

State 6 types of quark/anti-quark and their corresponding charge, baryon number and strangeness

Answer 29

Up quark (u) +2/3e, +1/3, 0
Down quark (d) -1/3e, +1/3, 0
Strange quark (s) -1/3e, +1/3, -1
Anti-up quark (ubar) -2/3e, -1/3, 0
Anti-down quark (dbar) +1/3e, -1/3, 0
Anti-strange quark (sbar) +1/3e, -1/3, 1

Question 30

Give three examples of leptons

Answer 30

Electrons, positrons and neutrinos

Question 31

State the β- decay equation for a neutron in terms of particles, and in quark notation

Answer 31

neutron -> proton + electron + anti-neutrino
or n -> p + e- + 𝜈bar
udd -> uud + e- + 𝜈bar
or d -> u + e- + 𝜈bar

Question 32

State the β+ decay equation for a proton in terms of particles, and in quark notation

Answer 32

proton -> neutron + positron + neutrino
or p -> n + e+ + 𝜈
uud -> udd + e+ + 𝜈
or u -> d + e+ + 𝜈

Question 33

State and define the two types of meson

Answer 33

Pion - meson not consisting of either a strange or anti-strange quark
Kaon - meson with one strange or one anti-strange quark

Question 34

State the quark model of the proton and neutron

Answer 34

Proton - uud
Neutron - udd

Question 35

Define half-life

Answer 35

The half-life, t1/2 of a radioactive isotope is the average time it takes for half of the number of active nuclei in the sample to decay.

Question 36

Define activity (A) of a radioactive isotope, and state its unit

Answer 36

Activity of a radioactive isotope is the number of nuclei of the isotope that disintegrate per second

Unit - becquerel (Bq)

Question 37

Define decay constant, and state its unit

Answer 37

The decay constant, λ, is the probability of an individual nucleus decaying per second

Unit - s^-1

Question 38

State the equation for activity

Answer 38

A = λN
Where λ is the decay constant and N is the number of undecayed nuclei

Question 39

State the exponential decay equations for number of undecayed nuclei (N), mass of a radioactive isotope (m), and activity of a radioactive isotope (A)

Answer 39

N = N₀e^-λt
m = m₀e^-λt
A = A₀e^-λt

Question 40

Derive an equation that relates decay constant (λ) and half-life (t1/2)

Answer 40

We know that N = N₀e^-λt
When t = t1/2, N = N₀/2
So N₀/2 = N₀e^-λt1/2
1/2 = e^-λt1/2
ln(1/2) = -λt1/2
ln2 = λt1/2
t1/2 = ln2/λ

Question 41

What is rest energy?

Answer 41

Rest energy is the energy due to rest mass m₀ and is given by Einstein’s mass-energy equation

E = m₀c²

Question 42

Describe and explain pair production

Answer 42

A very high energy gamma photon can change into a particle-antiparticle pair. Pair production is only possible when the photon has energy equal to or greater than the rest energy of the particle/antiparticle.
In other words, a single gamma photon with energy in excess of 2m₀c² can produce a particle-antiparticle pair, each of mass m

Question 43

Define binding energy

Answer 43

Binding energy of a nucleus is the work which must be done to separate the nucleus into its constituent neutrons and protons.

Question 44

Define mass defect

Answer 44

Mass defect (∆m) of a nucleus is the difference between the mass of the separated nucleons and the mass of the nucleus

Question 45

Explain why separate nucleons have a greater mass than the original nucleus

Answer 45

As work is done in separating the nucleus into its constituent parts, more energy is “stored” as potential energy in the separate parts than the original nucleus.
Using E = m₀c², if the separate nucleons have more energy, they must also have more mass

Question 46

Define binding energy per nucleon

Answer 46

The binding energy per nucleon of a nucleus is the average work done per nucleon to remove all the nucleons from a nucleus. This is a measure of the stability of the nucleus.