U238 and U235 occur in nature in an atomic ratio 140 : 1. Assuming that at the time of earth’s formation the two isotopes were present in equal amounts. If the age of the earth is n × 107 years, then find the value of n. (Round off to the nearest integer)[half-life of U238 = 4.5 × 109 yrs, half-life of U235 = 7.13 × 108 yrs , ln⁡140ln⁡2=7.13]

N238=N0e−λ238TN235=N0e−λ235T⇒1401=e(λ235−λ238)TT=604.1×107 yrs

Book Online Demo

Check Your IQ

Try Test

Courses

Offline Centres

$U^{238} a n d U^{235}$ occur in nature in an atomic ratio 140 : 1. Assuming that at the time of earth’s formation the two isotopes were present in equal amounts. If the age of the earth is n × 10⁷ years, then find the value of n. (Round off to the nearest integer)
[half-life of U²³⁸ = 4.5 × 10⁹ yrs, half-life of U²³⁵= 7.13 × 10⁸ yrs , $\frac{\ln 140}{\ln 2} = 7.13$ ]

see full answer

21% of IItians & 23% of AIIMS delhi doctors are from Sri Chaitanya institute !!

An Intiative by Sri Chaitanya

answer is 604.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

$\frac{N_{238} = N_{0} e^{- λ_{238} T}}{N_{235} = N_{0} e^{- λ_{235} T}} \Rightarrow \frac{140}{1} = e^{(λ_{235} - λ_{238}) T}$

$T = 604.1 \times 10^{7} y r s$

Watch 3-min video & get full concept clarity