1.

The radium and uranium atoms in a sample of uranium mineral are in the ratio of 1 : 2.8 xx 10^(6). If half-life period of radium is 1620 years, the half-life period of uranium will be

Answer»

`45.3 XX 10^(9)` years
`45.3 xx 10^(10)` years
`4.53 xx 10^(9)` years
`4.53 xx 10^(6)` years

Solution :According to radioactive equilibrium `lamda_(A) N_(A) = lamda_(B) N_(B)`
or `(0.693 xx N_(A))/(t_(1//2) (A)) = (0.693 xx N_(B))/(t_(1//2) (B)) [LAMDA = (0.693)/(t_(1//2))]`
Where `t_(1//2) (A) and t_(1//2) (B)` are half periods of A and B RESPECTIVELY
`:. (N_(A))/(t_(1//2)(A)) = (N_(B))/(t_(1//2)(B)) or (N_(A))/(N_(B)) = (t_(1//2) (A))/(t_(1//2)(B))`
`:.` At equilibrium Aand B are present in the ratio of their half lives `(1)/(2.8 xx 10^(6)) = (1620)/("Half-life of uranium")`
`:.` Half-life of uranium
`2.8 xx 10^(6) xx 1620 = 4.53 xx 10^(9)` years


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