Chapter 26 - Radioactivity

Question 1

Describe Rutherford’s scattering experiment.

Answer 1

Rutherford designed an experiment to investigate the distribution of positive matter in the atom.
Rutherford fired a narrow beam of alpha radiation (positive alpha particles) at a thin sheet of gold foil and observed deflections.
Most alpha particles passed straight through however, a small proportion of particles were deflected.

Question 2

What were the main conclusions Rutherford made from his scattering experiment?

Answer 2

• Most of the atom’s mass is concentrated in a small region in the centre (the nucleus)
• The nucleus is positively charged
• Electrons orbit the nucleus

Question 3

What model of the nucleus was used before Rutherford’s scattering experiment?

Answer 3

The plum-pudding model.

Thomson thought that the atom was made of small pieces of negatively charged matter speckled within a large piece of positively charged matter.

Question 4

What is the relationship between the probability of deflection of each layer of gold foil and the ratio of area of nucleus to the area of an atom?

Answer 4

They are equal,

d^2/D^2 = 1/10000n

where n is number of layers and d is diameter of nucleus, and D is diameter of atom.

Question 5

How can the radius of a nucleus be estimated from the closest approach of alpha particles?

Answer 5

Total energy of alpha particle = Ek + Ep (electric)

Initially we accelerate the alpha particle at high speed with a known initial velocity and initial kinetic energy.

As the alpha particle approaches the nucleus, it slows down due to the positive charge of the nucleus repelling the positive charge of the alpha particles (Electromagnetic force increases with distance) (Ek → Ep).

The maximum Ep of the alpha particle (at closest approach (distance from nucleus of alpha particle where Ek = 0)) is equal to the initial Ek of the alpha particle.

d = Qq/4π𝜀0Ek

where d = distance of closest approach = nuclear radius

Question 6

Describe the trend in ionisation power and range of alpha, beta and gamma radiation.

Answer 6

Alpha, Beta, Gamma
→ Range (in air: few cm, few m, infinite (intensity falls with increase in distance from source))
← Ionisation power

Question 7

What materials can be used to stop/absorb alpha, beta and gamma radiation?

Answer 7

Alpha - thick paper or thin metal foil
Beta - few mm of aluminium
Gamma - few cm of lead (most will be absorbed)

Question 8

How can we identify what types of radiation a source emits?

Answer 8

By placing different materials between the source and a Geiger-Muller tube and measuring the amount of radiation that passes through.

Question 9

Give some examples of sources of background radiation.

Answer 9

Rocks,
Cosmic rays,
Nuclear waste

Question 10

What is intensity in terms of radiation?

Answer 10

The radiation energy per second passing through a unit area.

Question 11

What is the intensity of radiation at a certain distance from the source as an equation?

Answer 11

I = E/4πr^2 = nhf/4πr^2

where E is total energy and n = number of photons

I = k/x^2

I ∝ 1/x^2

where x is the distance from the source.

Question 12

What should be subtracted from count-rate calculations?

Why should you do this?

Answer 12

Background radiation

To improve accuracy

Question 13

What is an equation for count-rate?

Answer 13

Count-rate = k/d^2

Question 14

What are the dangers of radioactivity?

Answer 14

Radiation can affect living tissue by damaging cells and DNA. Cell membranes can be destroyed by high exposure to radiation, killing the cells.

DNA molecules can be damaged and cells can mutate due to the ionising effects of radiation which can cause uncontrollable cell replication, forming a potentially cancerous tumour even at low exposure.

Question 15

What are examples of safe handling of radioactive sources?

Answer 15

• Keep inside lead containers
• Handle using tongs and gloves
• Source should spend minimum amount of time required outside of container to minimise exposure.

Question 16

What is nuclear decay?

Answer 16

When unstable nuclei emit ionising radiation to become more stable.

Question 17

LEARN ALPHA, BETA+ AND - DECAY AND ELECTRON CAPTURE EQUATIONS.

Answer 17

LEARN ALPHA, BETA+ AND - DECAY AND ELECTRON CAPTURE EQUATIONS.

Question 18

Radioactive decay is ______ and _________.

Answer 18

Radioactive decay is random and spontaneous (unaffected by external conditions).

Question 19

What is the activity of a radioactive sample?

What is the unit?

Answer 19

The rate of radioactive decay.

Unit: Becquerel, Bq OR decays per second

Question 20

What is the decay constant?

Answer 20

The probability of a given nucleus decaying per second.

Unit: s^-1

Question 21

What is the equation for the rate of radioactive decay?

Answer 21

ΔN/Δt = -λN

Question 22

The count-rate is __________ to the activity.

Answer 22

The count-rate is proportional to the activity.
A ∝ C
A = kN

Question 23

What is the half-life of a radioactive sample?

Answer 23

The time it takes for half of the radioactive nuclei in the sample to decay.
The time it takes for the activity or count-rate of a radioactive sample to halve.

Question 24

How can you calculate the nuclear radius of a material?

Answer 24

By electron diffraction. The results of electron diffraction of different nuclei show:

R = r0A^1/3

where R is nuclear radius, r0 is radius of nucleon and A is nucleon number.

Question 25

How can you calculate nuclear density?

Answer 25

ρ = m/v

V(nucleus) = 4/3πR^3
= 4/3π(r0A^1/3)
= 4/3πr0^3A

m(nucleus) = Am
where A is nucleon number and m is mass of nucleon

Add the equations to the equation for density to find nuclear density.

Nuclei of all atoms have the same density.

Question 26

How can you find the nuclear radius by electron diffraction?

Answer 26

sinθ = (1.22λ)/2r

r = 1.22λ/2sinθ

Question 27

What is the typical radius of a nucleus?

Answer 27

1x10^-15m