Question

In U²³⁸ ore containing Uranium the ratio of U²³⁴ to Pb²⁰⁶ nuclei is 3. Assuming that all the lead present in the ore is final stable product of U²³⁸. Half life of U²³⁸ to be 4.5 × 10⁹ years and the age of ore is ______ × 10⁹ years. (in 10⁹ years)

Options

• 2

• 4

• 6

• 8

Answer 1

In U²³⁸ ore containing Uranium the ratio of U²³⁴ to Pb²⁰⁶ nuclei is 3. Assuming that all the lead present in the ore is final stable product of U²³⁸. Half life of U²³⁸ to be 4.5 × 10⁹ years and the age of ore is 2 × 10⁹ years. (in 10⁹ years)

Explanation:

`"N"/("N"_0-"N") = 3/1`

⇒ `"N"/"N"_0 = 3/4`

`"N"/"N"_0 = 3/4 = "e"^(-lambda"t")` 

λt = log_e 4/3

⇒ t = `((log_e4//3)/0.693)` T_1/2

t = `4.5xx10^9[.1249/.3010]`

= 1.8678 × 10⁹ years

≈ 2 × 10⁹ years