8.2 - Radioactive Decay

Question 1

What is the definition of 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.

Question 2

Is the rate of decay affected by the surrounding conditions?

Answer 2

No, radioactive decay is a random process

Question 3

What is the only thing you can estimate with radioactive decay?

Answer 3

The proportion of nuclei decaying in a given time period (the half life).

Question 4

What does the count rate of a GM tube represent?

Answer 4

The number of decays.

Question 5

What do the fluctuations in the count rate of a GM tube provide?

Answer 5

Evidence for the randomness of radioactive decay.

Question 6

What is the decay constant? (λ)

Answer 6

The probability that an individual nucleus will decay per unit of time.

Question 7

What is the suggested activity rate of a sample that is highly radioactive?

Answer 7

It has a high level of activity.

Question 8

What is the equation for calculating the activity of a radioactive source?

Answer 8

A = - ΔN /Δt = λN
A = activity of the sample (Bq)
ΔN = number of decayed nuclei
Δt = time interval (s)
λ = decay constant (s⁻¹)
N = number of nuclei remaining in a sample

Question 9

What is the activity of a sample measured in?

Answer 9

Becquerels (Bq)
1 Bq = one decay per second (1s⁻¹)

Question 10

What are 3 things the equation calculating activity show?

Answer 10

• The greater the decay constant, the greater the activity (of the sample)
• The activity depends on the number of un-decayed nuclei remaining in the sample
• The minus sign indicates that the number of nuclei remaining decreases with time

Question 11

What is the shape of a graph that shows the number of un-decayed nuclei against time?

Answer 11

Negative exponential decay. (starts high on the y axis).

Question 12

From the graph of un-decayed nuclei against time, what shows a smaller decay constant?

Answer 12

If the exponential decay line is shallower.

Question 13

What is the symbol for the initial number of un-decayed nuclei?

Answer 13

N₀

Question 14

What is the equation for the number of un-decayed nuclei within a certain time?

Answer 14

N = N₀e^–λt
N = number of un-decayed nuclei at a certain time t
N₀ = the initial number of undecayed nuclei (When t=0)
λ = decay constant (s⁻¹)
t = time interval (s)

Question 15

Using the equation for finding the number of un-decayed nuclei, what other quantities can you substitute in and why?

Answer 15

A = A₀e^–λt
activity - directly proportional to N (number of un-decayed nuclei)
C = C₀e^–λt
count rate - related to activity of the sample

Question 16

What is the inverse function of e^x?

Answer 16

ln(y) (natural log)
e^x = y
x = ln(y)

Question 17

What is Avogadro’s constant?

Answer 17

6.02 x 10²³mol⁻¹
(The number of atoms in one mole of a substance)

Question 17

How do you get the number of nuclei using Avagadro’s constant? (equation)

Answer 17

Number of nuclei =
(mass x (6.02 x 10²³)) / molecular mass

Question 18

What is half-life?

Answer 18

The time taken for the initial number of nuclei to halve for a particular isotope.

Question 18

What is the equation for half-life?

Answer 18

𝑇½ = ln 2 / λ
𝑇½ = half life
ln 2 = natural log 2
λ = decay constant

Question 18

How do you find the decay constant from a activity/time graph?

Answer 18

Find the half-life (where the activity halves) then put it into the equation
𝑇½ = ln 2 / λ

Question 18

How do you calculate the number of atoms remaining after a certain time (on an activity/time graph)?

Answer 18

Find the activity at time t.
Use the equation A = λN to calculate N

Question 18

What is the most common isotope used in carbon dating?

Answer 18

Carbon-14

Question 19

What is carbon dating?

Answer 19

A highly reliable ageing method that predicts the age of organic materials/organisms.

Question 20

What is the time period in which carbon dating is effective?

Answer 20

Around 1000 years to a limit of 40 000 years.

Question 21

Why is carbon dating not possible if 1000 years haven’t passed?

Answer 21

The activity is too high so it is difficult to accurately measure the small change in activity.

Question 22

Why is carbon dating not possible after 40000 years has passed?

Answer 22

The activity will be too small and have a count rate similar to background radiation.

Question 23

How is radioactive waste stored?

Answer 23

In water tanks or sealed underground.

Question 24

Why must radioactive waste be stored so effectively?

Answer 24

Because of the long half-lives of the isotopes used, the waste is radioactive for a long time after use (and is still harmful).

Question 25

How would you interpret N = N₀e⁻λᵗ as a straight line graph equation?

Answer 25

y = mx + c
ln(N) = ln(N₀) -λt
ln(N) = y axis
ln(N₀) = y intercept
t = x-axis
-λ = gradient

Question 26

How has potassium-argon dating occcured?

Answer 26

ancient rocks contain trapped argon gas as a result of the decay of the radioactive isotope of potassium-40.
This happens when a potassium nucleus captures an inner shell electron (electron capture).

Question 27

What are the decay equations of potassium-argon dating?

Answer 27

electron capture:
⁴⁰K + e⁻ –> ⁴⁰Ar + Ve
potassium isotope can also decay by B⁻ emission
⁴⁰K –> ⁴⁰Ca + B⁻ + /Ve/ (/Ve/ = anti-neutrino)

Question 28

What is potassium-argon dating used for?

Answer 28

Potassium-40’s half-life is 1.25 BILLION years.
The age of the rock (when its solidified) can be calculated by measuring the proportion of argon-40 to potassium-40.
It is used for dating rocks that are up to 100 million years old.

Question 29

What is uranium-lead dating used for?

Answer 29

Dating geologic events more than 100 million years old.

Question 30

How does uranium-lead dating work?

Answer 30

Uranium atoms decay whilst the number of lead atoms increases.
Uranium decays via a decay chain which ends with lead-206 (a stable isotope)

Question 31

Why is uranium-lead dating the most accurate?

Answer 31

Uranium has been studied a lot more and its decay constant is better known than other isotopes, therefore it is more accurate.