Rate of Radioactive Decay Flashcards
what is a decay constant
- the probability that a nucleus will decay
- measured per second
why do we need a decay constant, with the key word being “constant”
- because radioactive decay is spontaneous and random
- so a constant is used to give an average rate of expected decay
what is the symbol for the decay constant
lambda (Y)
what is activity (A)
- the number of radioactive decays
- per unit of time
if N is the number of nuclei in a sample, how would A be written in terms of N
A = dN / dt
what is the equation relating A and Y
A = -YN
why is there a -ve sign
- 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
what unit is activity measured in
Bq
what is the formula for the number of remaining nuclei in a sample after time t
N = N(0) * e^(-Yt)
what are the variables in that equation
- N = remaining number of nuclei
- N(0) = initial number of nuclei
- Y = decay constant
- t = time (s)
how does the activity of a sample of nuclei change overtime
it gradually decreases
why does the activity decrease overtime
- 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
what is the technical name given to the measure of the rate of decrease of activity
half-life
what is one half-life
- 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
what is the equation for what Y would equal when 1 half-life had passed, and why would it simply be like this
- Y = ln2 / t
- because you just say that N = 1/2 N(0) and rearrange for Y
what is the equation for calculating activity over a certain period of time
A = A(0) e^-Yt
what would graph of activity against time look like
- the half-life graph were all used to
- the 1 / x shaped graph
how would you use this graph to work out the half-life of a sample
by lining up the point where the activity halves with the time on the x axis
in an ideal world, what should the subsequent half-lives for 1 graph have in common
the time between each half life should be the same
why isnt this the case in reality however
- because of the random nature of radioactive decay
- combined with experimental and graphing errors
what is the most efficient way of counteracting this in order to get a more accurate half-life value
- by recording the half-life on a graph multiple times
- and calculating an average with it
what would you do the activity equation so you could draw a straight line graph with the data collected
ln the equation
what would be the ln’d equation in the form y = mx + c
lnA = -Yt + lnA(0)
what would the axes on the graph be
lnA against t
what would m and c be
- m = the decay constant, Y
- c = lnA(0)
