Nuclear Physics 2

Question 1

Define activity of a radioactive isotope

Answer 1

The number of nuclei of the isotope that decay per second

The rate of change of the number of nuclei per second

Question 2

What is the unit for activity

Answer 2

Becquerel - Bq

1 disintegration per second

Question 3

How to calculate the activity of an isotope

Answer 3

A = λ N

λ = Decay constant

N = No. of nuclei

Question 4

How to calculate Half Life

Answer 4

T_1/2 = ln2 / λ

Question 5

What is the relationship between Activity and No. of nuclei

Answer 5

They are proportional

A = λN

Question 6

How are objects dated

Answer 6

Measuring the amount of carbon 14 in the object and comparing it to the initial amount, the percentage of which is roughly the same across all living things

Question 7

Explain the use of Technetium 99m

Answer 7

Technetium-99m is a pure gamma emitter

Gamma rays can be easily detected by a gamma camera and are only very weakly ionising

Has a half life of 6 hours, which is short enough to limit exposure but long enough for tests to be carried out, and it can be easily prepared on site.

Used as a tracer in medicine

Question 8

Explain the forces acting on nucleons in the nucleus

When does a nucleus become unstable

Answer 8

The strong nuclear force is an attractive force that acts between all the nucleons, keeping them together

Then the electromagnetic force acts between the protons (which are charged) and is repulsive

A nucleus becomes unstable when these 2 forces are unbalanced

Question 9

Name the 4 reasons for a nucleus becoming unstable

Answer 9

Has too many neutrons

Too many protons

Too many nucleons

Too much energy

Question 10

Explain what happens when a nucleus has too many neutrons

Answer 10

Beta Minus decay

One of the neutrons turns into a proton and then a beta minus particle and anti-neutrino are emitted

Nucleon number is constant, proton number increases by 1

Question 11

Explain what happens when a nucleus has too many protons

Answer 11

Beta plus decay

or, Electron capture

Beta plus - Proton turns into a neutron and then a beta plus particle and neutrino are emitted

Electron Capture - An orbiting electron is taken into the nucleus and combines with a proton to form a neutron. Then a neutrino is emitted

Proton number decreases by 1, nucleon number doesn’t change

Question 12

Explain what happens when a nucleus has too many nucleons

Answer 12

Alpha Emission

An alpha particle - 2 protons and 2 neutrons is emitted

Nucleon no. decreases by 4, proton number decreases by 2

Question 13

Explain what happens when a nucleus has too much energy

Answer 13

Decays through gamma emission

Usually occurs after another type of emission, that causes the nucleus to have excess energy and become excited

Question 14

How does activity/half-life affect how radioactive nuclei are stored

Answer 14

• Nuclei with extremely long half lives have to be stored in steel casks deep underground
• To prevent these nuclei from damaging the environment and the people that may be living around them hundred of years into the future

Question 15

Graph of no. of Protons against no. of Neutrons

What does it show

Answer 15

The number of neutrons and protons in a stable nucleus does not increase uniformly beyond around 20 of each neutrons and protons.

Question 17

Explain the reason behind what is shown in a graph of no. of protons against no. of neutrons

Answer 17

The electromagnetic force of repulsion between protons becomes larger than the strong nuclear force keeping the nucleus together

So more neutrons are needed to increase the distance between protons in order to decrease the magnitude of the electromagnetic force to keep the nucleus stable.

Question 18

How to estimate the radius of a nuclear atom

Answer 18

Calculate the distance of closest approach

Question 19

How to calculate the distance of closest approach

Explain why

Answer 19

The point at which the particle stops and has no kinetic energy

Its electrical potential energy is equal to its initial kinetic energy due to conservation of energy.

As a positively charged particle moves towards a positively charged nucleus it will experience an electrostatic force of repulsion and slow down as its kinetic energy is converted to electric potential energy.

Question 20

Explain how to calculate nuclear radius using electron diffraction

Answer 20

• Accelerate electrons to a high speed so their De Broglie wavelength is around x10^-15
• Direct electrons at thin film in front of a screen so they diffract through the gaps between nuclei and form a diffraction pattern
• Diffraction pattern is concentric circles that get dimmer the further out, plot a graph of intensity against diffraction angle and find angle of first minimum
• From angle of first minimum, calculate nuclear radius

Question 21

Formula to calculate nuclear radius from the angle of the first minimum in a diffraction pattern

Answer 21

sin θ = 0.61λ / R

Question 22

Relationship between nuclear radius and nucleon number, include a graph and the formula

Answer 22

Exponential

R = R₀A^1/3

A = No. of nucleons

R = Radius

Question 23

What is a typical value for nuclear radius

Answer 23

1 x 10^-15m

Question 25

Show that the density of a nucleus is a constant value

Answer 25

Density = mass/volume

D = A x m_nucleon / (4/3πR³)

= A x m_nucleon / (4/3π(R₀A^1/3)³)

= A x m_nucleon / (4/3π(R₀³A))

= m_nucleon / (4/3π R₀³)

= constant value, A and R (both variable factors) cancelled out

Question 26

Formula for calculating density of a nucleus

Answer 26

Density = m_nucleon / (4/3π R₀³)