How long will a 16.0 g sample of bismuth-210 take to decay to 2.0 g if its half-life is 5

days?

A total of 15 days are required to reduce the sample from 16 g to 2 g.

Explanation:

It is known that after half life time, the concentration of the sample will get reduced to half. So 16 g of Bismuth-210 will reduce to 8 g, which is the half of the initial gram taken, after completion of first half life time period. So here, the half life time period of Bismuth-20 is given as 5 days.

It means after a gap of 5 days, the initial concentration of weight of sample will reduce from 16 g to 8g. But the problem asked to find the number of days required to reduce the sample concentration from 16 g to 8 g. So again if we keep the sample for 5 days, it will disintegrate to 4 g from 8 g. Thus, a total of 10 days now, reduced Bismuth from initial 16 g to 4 g.

Again, if we keep it for 5 days, then the concentration will be reduced to 2g. So after keeping the sample for 15 days which contains three times its half life period, the sample will have a reduction in their concentration from

16 g to 2 g.

Thus, a total of 15 days are required to reduce the sample from 16 g to 2 g.