Calculation of true thickness of the bed

 Question: The Decay Constant of ²³⁵ U and ²³⁸ U are 9.848 * 10^-10 /year and 1.551* 10^-10 /year respectively. Calculate the half-life of the Uranium isotopes.

Solution:

We know the relation between the half-life and the decay constant is

$t_{1/2}=\frac{ln(2)}{\lambda}=\frac{0.693}{\lambda}$

 For

1. The Half-life of the Uranium 235 isotope is

 

$t_{1/2}=\frac{0.693}{9.848\times 10^{-10}}=0.070\times 10^{10}$

 

2. The Half-life of Uranium 238 isotope is

 

        $t_{1/2}=\frac{0.693}{1.551\times 10^{-10}}=0.4468\times 10^{10}$