The activity of a radioactive sample consisting of a single
radioactive isotope is given by:
A = ?*N
where ? is the decay constant of the isotope and N is the number of
atoms of the isotope in the sample.
The decay constant and halflife (T) of a radioactive isotope are
related by:
? = ln(2)/T
so,
A = ln(2)*N/T
The atomic mass of K is 39.1 gm/mol, so 380 mg = 0.38 gm of K is
9.72*10^-3 moles of K.
Multiplying by Avogadro's number, this many moles contains:
(9.72*10^-3 moles)*(6.022*10^23 atoms/mol) = 5.85*10^21
atoms.
40K makes up just 0.012% of all the atoms in a modern sample of
ordinary potassium, so there are about:
0.00012*5.85*10^21 atoms = 7.02*10^17 atoms of 40K in a typical
banana.
The activity of 40K in a typical banana is then given by:
A = (7.02*10^17 atoms)*ln(2)/(4.04*10^16 sec)
A = 12 atoms decaying/second
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