1.

The isotopes of U^(238) and U^(235) occur in nature in the ratio 128 : 1. Assuming that at time of earth's formation, they were equal in ratio, make an estimate of age of earth. The half lives of U^(238) and U^(235) are 4.5 xx 10^9 yrs and 7.13 xx 10^8 yrs respectively:

Answer»

`2.2 xx 10^(7) yrs`
`3.4 xx 10^(8) yrs`
`5.9 xx 10^(9) yrs`
`6.5 xx 10^(10) yrs`

Solution :`N=N_(0)e^(-LAMBDA t), N_(1)e ^(-(ln 2)/(Ti))t)`
`N_(2)=N_(0) e^(-(ln2)/(T_(2))t`
`N_(1)/N_(2) approx e^(ln 2) (1/T_(2)-1/T_(2))t`
`128 =e^(ln 2) (1)/(7.13 xx 10^(8))-(1)/(4.5 xx 10^(9))t`
`or ln 2^(7) =ln 2 xx 1.18 xx 10^(-9)t`
`RARR 7 ln 2=ln 2 xx 1.18 xx 10^(-9)t`
`rArr t=(7)/(1.18) xx 10^(9) =5.9 xx 10^(9)yrs.`


Discussion

No Comment Found

Related InterviewSolutions