c) Activity

d) activity of a source; decay constant λ of an isotope; A = λN

ei) half-life of an isotope; λt(1/2) = ln(2)

fi) the equations A = A0e^-λt and N = N0e^-λt, where A is the activity and N is the number of undecayed nuclei

half-life = time taken for half of the radioactive nuclei in a sample to decay

• the number of undecayed nuclei decreases exponentially with time

activity = the rate of nuclei decay

decay constant = the probability of a radioactive nucleus decaying per unit time

A = λN

• activity (Bq) = decay constant (s-1) x number of undecayed nuclei

A ∝ N

λt(1/2) = ln(2)

• decay constant (s-1) x half-life of the isotope (s) = natural logarithm of 2

λ ∝ 1/t(1/2)

N = N0e^-λt

• number of undecayed nuclei = initial number of undecayed nuclei x e^-decay constant (s-1) x time (s)

A = A0e^-λt

• activity (Bq) = initial activity (Bq) x e^-decay constant (s-1) x time (s)