9.7 Half Life - NC

Question 1

What is half life?

Answer 1

average time for a given number of radioactive nuclei of that isotope to decay to half of that time

Question 2

Which simple classroom experiment can be used to model half life?

Answer 2

Having a set number of dies with one side being marked off. After being thrown onto a box, all dies facing upwards with the marked off side are said to be decayed and hence removed. This is repeated until there is 0 dice.

Question 3

If we made a graph of Dies/turns what type of graph will we get?

Answer 3

an exponential graph (a decay one)

Question 4

Why is this similar to radioactivity? and how is this shown on a graph?

Answer 4

It is an exponential graph, however it is not fully smooth as number of turns isn’t continuous

Question 5

How can we make the graph smoother?

Answer 5

If we combined the results with more people in the class.

Question 6

Is radioactive decay a truly random process? How is this shown?

Answer 6

Yes

By having an average value for the half life, as it will be slightly different each time

Question 7

How does actual radioactive decay vary from the dice throwing experiment?

Answer 7

Radioactivity is continuous.

Question 8

What is the equation for radioactive decay that is similar to discharging/charging a capacitor? In terms of undecayed nuclei left

Answer 8

N = N0e^-λt

Question 9

What is that equation in terms of activity?

Answer 9

A = A0e^-λt

Question 10

What is the equation in terms of count rate?

Answer 10

C = C0e^-λt

Question 11

What do these symbols stand for?

Answer 11

N = number of undecayed nuclei  
A = activity 
C = count rate 
(N or A or C)0 = initial 
λ = decay constant 
t = total time elapsed

Question 12

Equation for half life?

Answer 12

ln2/Λ = t 
t = half life 
Λ = decay constant  
ln2 = constant value

Question 13

Why is half life important when considering nuclear reactors?

Answer 13

As some products of fusion in nuclear reactors may have a long half life, which would mean reprocessing or safe disposal would be dangerous and potentially costly.

Question 14

How can we find half life from an exponential graph? for example of undeceyed nuclei against time or activity against time or count rate against time.

Answer 14

We half the peak of the y-axis (undeceyed nuclei,count rate,activity) to half that number and read off time. This should be done for a quarter, eighth and so on to check the value is consistent.

Question 15

How can we measure the radioactivity of protactinium-234?

Answer 15

We have a setup of geiger muller tube, a geiger counter and a protactinium generator.
1 - Shake the protactinium generator
2 - Wait for layers in the generator to separate. The protactinium will be in the top layer. Point the geiger muller tube at the top layer.
3 - Record count rate as soon as layers are seperated (counts in ten seconds) and repeat at a regular interval (e.g. 30 seconds)
4 - Once the data has been collected. Leave the bottle for at least 10 minutes. Then make the count again. This will be the count for background radiation.
5 - Subtract background radiation count for all collected data. Plot a graph of count rate against time. We should end up with an exponential graph. Find half life .

Question 16

What is a protactinium generator?

Answer 16

A bottle containing uranium salt, two solvents and the constituents of uranium decay(including protactinium 234). These seperate into layers.

Question 17

What happens to an exponential graph if we take LN of the values and re plot it ?

Answer 17

It becomes a straight line

Question 18

Rearrange N = N0e^-λt so that it is in the form y = mx+ c using natural logs.

Answer 18

Ln N = Ln N0 - λt 
where 
y = Ln N 
c = Ln N0 
m = -λ 
x = t

Question 19

How do we derive Ln2/ λ = t?

Answer 19

N = N0e^-λt
N/N0 = e^-λt 
No/n = 1/e^-λt 
N0/N = e^λt 
if N1/2 = N0/2 
N0/N0/2 = e^λt 
2 = e^λt 
Ln2 = λt 
Ln2/λ = t  
where t = half life 
and λ = decay constant