Uranium ores contain one radium `-226` atom for every `2.8 xx 106` uranium `-238` atoms. Calculate the half-life of `._92 U6238` given that the half-life of `._88 Ra^226` is `1600` years `(._88Ra^226` is a decay product of `._92 U^238`) :

Options

A. `1.75 xx 10^3 years`
B. `1600 xx (238)/(92) years`
C. `4.5 xx 10^9 years`
D. `1600 years`

Answer

C

Explanation

( c) `N_1 lamda_1 = N_2 lamda_2`
`T = (0.693)/(lamda)`
Hence `2.8 xx 10^6 xx (0.693)/(T_1(U)) = 1 xx (0.693)/(T_2 (Ra))`
`:. T_1 (U) = 1600 xx 2.8 xx 10^6`
`=4.48 xx 10^9` years
`~~ 4.5 xx 10^9` years.