The analysis of a uranium reveals that ratio of mole of `.^(206)Pb`and `.^(238) U` in sample is 0.2 . If effective decay constant of process `.^(238)U rarr .^(206) Pb` is `lambda` then age of rock is

Options

A. `(1)/(lambda) In (5)/(4)`
B. `(1)/(lambda) In ((5)/(1))`
C. `(1)/(lambda) In(4)/(1)`
D. `(1)/(lambda) In ((6)/(5))`

Answer

D

Explanation

In the rock `("Moles of ".^(206)Pb)/("Moles of " .^(238 )U)=0.2=(0.2)/(1)`
`{:(,.^(238)U,rarr,.^(206)Pb,),("Initial moles",1.2 "mole*",,0,"(*calculate by moles of"),(,1"mole",,0.2 "mole","U left & moles of Pb formed) "):}`
`" " t=(1)/(lambda) ln ((1.2)/(1))=(1)/(lambda)ln ((6)/(5))`