Discussion Forum

The half-life for $\alpha$- decay of uranium  ₉₂ U²²⁸ is  047 x10⁸ yr. If a rock contains 60% of original ₉₂ U²²⁸  atoms , then its age is [ take log 6= 0.7787 , log 2= 0.3]

Answer:

Explanation:

Given:  T_1/2 =4.47 x 10⁸

 $\Rightarrow \frac{N}{N_{0}}=\frac{60}{100}=\left(\frac{1}{2}\right)^{n}\Rightarrow 2^{n}=\frac{10}{6}$

 Apply  logarithm on both sides

 n log 2= log 10-log 6

 $\Rightarrow$   n x 0.3 = 1-0.778=0.22

$\Rightarrow n=\frac{0.222}{0.3}=0.74$

 So,  t = n T_1/2  =0.74 x 4.47x 10⁸

 or t = 3.3 x 10⁸ yr