Phosphorus-32 has a half life of 14.3 days. how many days will it take for radioactive sample to decay to 1/8 it's size?

43.3 days

Explanation:

Half-life of Phosphorus-32 = 14.3 days

First we have to calculate the rate constant, we use the formula :

Now we have to calculate the days for radioactive sample to decay to 1/8 it's size

Expression for rate law for first order kinetics is given by:

where,

k = rate constant  =

t = age of sample  = ?

a = let initial size  = 1

a - x = amount left after decay process  =

Now put all the given values in above equation, we get

Thus it will take 43.3 days for radioactive sample to decay to 1/8 it's size.