Phosphorus-32 has a half-life of 14.0 days. starting with 6.00 g of 32p, how many grams will remain after 112 days ?

The radioactive decay follows first order kinetics

For first order reaction the relation between rate constant half life is

K = 0.693 / t1/2

K = 0.693 / 14 = 0.0495 day^-1

The first order rate equation is

ln (A / At) = Kt

Where

A = initial amount

At = amount left at time t

t = time

K = rate constant

Putting values

ln (6 / At) = 0.0495 X 112

ln (6 /At) = 5.544

taking antilog

6 / At = 255.7

At = 0.0235 g

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