Q.13.25 A source contains two phosphorous radio nuclides and . Initially, 10% of the decays come from . How long one must wait until 90% do so?
Let initially there be N1 atoms of and N2 atoms of and let their decay constants be and respectively
Since initially the activity of is 1/9 times that of we have
(i)
Let after time t the activity of be 9 times that of
(ii)
Dividing equation (ii) by (i) and taking the natural log of both sides we get
where and
t comes out to be 208.5 days