Rate of Radioactive Decay

Question 1

what is a decay constant

Answer 1

• the probability that a nucleus will decay

- measured per second

Question 2

why do we need a decay constant, with the key word being “constant”

Answer 2

• because radioactive decay is spontaneous and random

- so a constant is used to give an average rate of expected decay

Question 3

what is the symbol for the decay constant

Answer 3

lambda (Y)

Question 4

what is activity (A)

Answer 4

• the number of radioactive decays

- per unit of time

Question 5

if N is the number of nuclei in a sample, how would A be written in terms of N

Answer 5

A = dN / dt

Question 6

what is the equation relating A and Y

Answer 6

A = -YN

Question 7

why is there a -ve sign

Answer 7

• because it is measuring the rate of decrease of N
• as it can also be written as dN/dt = -YN
• but he -ve sign is ignored incalculations

Question 8

what unit is activity measured in

Answer 8

Bq

Question 9

what is the formula for the number of remaining nuclei in a sample after time t

Answer 9

N = N(0) * e^(-Yt)

Question 10

what are the variables in that equation

Answer 10

• N = remaining number of nuclei
• N(0) = initial number of nuclei
• Y = decay constant
• t = time (s)

Question 11

how does the activity of a sample of nuclei change overtime

Answer 11

it gradually decreases

Question 12

why does the activity decrease overtime

Answer 12

• as more nuclei decay there will be less remaining to decay
• which would decrease the number of decays per second
• and therefore the activity of the sample

Question 13

what is the technical name given to the measure of the rate of decrease of activity

Answer 13

half-life

Question 14

what is one half-life

Answer 14

• the time it takes for half the atoms of a nuclide within a sample to decay
• aka the time it takes for the activity to half

Question 15

what is the equation for what Y would equal when 1 half-life had passed, and why would it simply be like this

Answer 15

• Y = ln2 / t

- because you just say that N = 1/2 N(0) and rearrange for Y

Question 16

what is the equation for calculating activity over a certain period of time

Answer 16

A = A(0) e^-Yt

Question 17

what would graph of activity against time look like

Answer 17

• the half-life graph were all used to

- the 1 / x shaped graph

Question 18

how would you use this graph to work out the half-life of a sample

Answer 18

by lining up the point where the activity halves with the time on the x axis

Question 19

in an ideal world, what should the subsequent half-lives for 1 graph have in common

Answer 19

the time between each half life should be the same

Question 20

why isnt this the case in reality however

Answer 20

• because of the random nature of radioactive decay

- combined with experimental and graphing errors

Question 21

what is the most efficient way of counteracting this in order to get a more accurate half-life value

Answer 21

• by recording the half-life on a graph multiple times

- and calculating an average with it

Question 22

what would you do the activity equation so you could draw a straight line graph with the data collected

Answer 22

ln the equation

Question 23

what would be the ln’d equation in the form y = mx + c

Answer 23

lnA = -Yt + lnA(0)

Question 24

what would the axes on the graph be

Answer 24

lnA against t

Question 25

what would m and c be

Answer 25

• m = the decay constant, Y

- c = lnA(0)