3.8.1.3 Radioactive decay

Question 1

What is radioactive decay?

Answer 1

The spontaneous disintegration of a nucleus to form a more stable nucleus, resulting in the emission of an alpha, beta or gamma particle.
It is a random and spontaneous process.

Question 2

What is meant by a random process?

Answer 2

Equal probability of any nucleus decaying.
Cannot be known which particular nucleus will decay next.
Cannot be known at what time a particular nucleus will decay.
Only possible to estimate the proportion of nuclei decaying in a given time period.

Question 3

What is meant by a spontaneous process?

Answer 3

One which happens without external influence *

Question 4

How can the random nature of decays be proven?

Answer 4

Using a Geiger-Muller tube
- when placed near a radioactive source, decays are found to be irregular and cannot be predicted. Each count represents a decay of an unstable nucleus. Fluctuations in count rate on GM tube provide evidence for the randomness of radioactive decay.

Question 5

What is the average decay rate?

Answer 5

The average number of nuclei that are going to decay per unit time

Question 6

What is the decay constant?

Answer 6

The probability that an individual nucleus will decay per unit time

Question 7

What is the formula for activity?

Answer 7

A = -∆N/∆t = λN

A: Activity (Bq, s^-1)
∆N: Number of decayed nuclei
λ: rate constant (s^-1)
N: number of remaining nuclei in sample

Question 8

What are the key features of the exponential decay graph?

Answer 8

Steeper the slope, the larger the decay constant.
The decay curves start on the y-axis at the initial number of undecayed nuclei

Question 9

What are the equations for exponential decay?

Answer 9

N=N_0e^(-λt)
N: number of undecayed nuclei
N_0: initial number of nuclei
A=A_0e^(-λt)
A: activity after decays
A_0: initial activity
C=C_0e^(-λt)
C: count rate after t
C_0: initial count rate

Question 10

What is the formula for the number of moles?

Answer 10

n = m/Mr

Question 11

What is the formula for the number of nuclei?

Answer 11

Number of nuclei = (m*N)/Mr

Question 12

What is the half-life?

Answer 12

The time taken for the initial number of nuclei to halve for a particular isotope. (hence activity is halved).

Question 13

How is the formula for half-life derived?

Answer 13

N = N_0e^(-λt)

1/2N_0 = N_0e^(λt)

hence 1/2 = e^(-λt)

-ln2 = -λt

t_1/2 = ln2/λ

Question 14

How are logs taken to plot half life curves?

Answer 14

N = N_0e^(-λt)

lnN = lnN_0 - λt

(in form y=mx+c)
- t is on the x-axis, y is lnN

Question 15

How is C-14 formed?

Answer 15

Cosmic rays knock out neutrons from nuclei, which collide with nitrogen in the air.
n + N-14 -> C-14 + p
Plants take in carbon dioxide from the atmosphere for photosynthesis, including the radioactive isotope C-14. They are then eaten by animals and humans - all living organisms absorb C-14, after they die, they do not absorb anymore. Proportion of C-14 is constant in living organisms as carbon is constantly being replaced when they are alive. When they die, the activity of C-14 starts to fall. Samples can be tested by comparing the current amount of C-14 with the initial amount (based on ration of C-14 to C-12)

Question 16

How reliable is carbon dating?

Answer 16

Reliable for samples around 1000 to 40000 years old.
If it is less than 1000 years old; the activity of the sample is too high. So difficult to measure small change in activity. Ratio C-14 and C-12 is too high.

If it is more than 40000 years old;
activity is too small, count rate is similar to background radiation. Ratio C-14 to C-12 is too small to determine age.

Question 17

What are types of radioactive dating?

Answer 17

Carbon dating
Potassium-Argon dating
Uranium-Lead dating

Question 18

Describe Potassium-Argon dating

Answer 18

Ancient rocks contain trapped argon gas as a result of the decay of the radioactive isotope K-40. This happens when a potassium nucleus captures an inner shell electron, also known as electron capture.
K-40 +e- -> Ar-40 +v_e
K-40 can also decay by beta - emission to form Ca-40
K-40 _> Ca-40 + β- + ve(anti)

Age of the rock can determined by measuRing the proportion of Ar-40 to K-40. Method accurate for rocks up to 100 million years.

Question 19

Describe Uranium-Lead dating

Answer 19

Useful for rocks over 100 million years.
Initially, there is only uranium in the rock, but it decays to lead-206 which is a stable isotope, through a decay chain. The ratio of Pb-206 to U-238 increases over time, which can be used to determine the age of the rock.
This is the most accurate technique, since Uranium’s decay constant is much better studied

Question 20

How is radioactive waste stored?

Answer 20

Waste products from nuclear power stations need to be stored for the time that they are radioactive e.g. in water tanks or sealed underground.