`U^238`decays to `(Pb)^206`with a half-life of `4.47xx10^9`y.The ratio of number of nuclei of pb to u 238 after a time of 1.5 .10 power 9 years given 21/3=1.26

Answer

A, B

Explanation

Half life period can be a single for all the
process. It is the time taken for (1)/(2) of the uranium to convert to lead
No of atons of
` U^(238) = (6 xx 10^(23 ) xx 2 xx 10^(-3))/(238) `
` = (12)/(238) xx 10^(20) `
` = 0.05042 xx 10^(20)`
Initially total no. of uranium atoms
` =((12)/(238) + (36)/(206)) xx 10^(20) `
`=0.06789`
` N= N_(0) e^(-lambda t) `
`rArr N = e^(-0.093/(t_1//2)`
`rArr 0.05042 = 0.06789 = e^ (-0.6931)/(4.47 xx10^(9)) `
` rArr log ((0.05042)/(0.06789)) = (-0.6931)/(4.47 xx10^(9)) `
` t = 1.92 xx 10^(9) year `