Half-Life/Disintegrations?

Question

For 1.9 mole of the radioactive isotope phosphorus-32, half-life = 14.3 days, how many disintegrations have occurred after 17 minutes?

Please give a little explanation.

Answer 1

you have the differential formula for desintegrations in a short time versus half life

dN/dt = -N0 k where k = ln2/half life

so dN = -N0 k dt

N0 = 1.9*6.0210^23 k = ln2/14.3*24*60, (in minutes)

dN = - 1.9*6.0210^23*17*ln2/14.3*24*60=
6.5410^20 desintegrations