A radioactive sample contains two different types of radioactive nuclei. A with half-life 5 days and B with half-life 30 days. Initially the decay rate of the A type nuclei is 64 times that of B type of nuclei. Their decay rates will be equal when time is 9n days. Find the value of n.

see full answer

Talk to JEE/NEET 2025 Toppers - Learn What Actually Works!

Real Strategies. Real People. Real Success Stories - Just 1 call away

An Intiative by Sri Chaitanya

answer is 4.

(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

Detailed Solution

Let at $t = 0, R_{B} = R_{0},$ then $R_{A} = 64 R_{0} (R = d e c a y r a t e)$

After time t, $R_{A} = (64 R_{0}) e^{- λ_{A} t}$ And $R_{B} = R_{0} e^{- λ_{B} t}$

Given, $R_{A} = R_{B}$

$∴ 64 R_{0} e^{- λ_{A} t} = R_{0} e^{- λ_{B} t}, 64 = e^{(λ_{A} - λ_{B}) t}$

$\Rightarrow {(2)}^{6} = e^{(λ_{A} - λ_{B}) t}$

$∴ 6 \ln (2) = (λ_{A} - λ_{B}) t$

$∴ t = \frac{6 (\ln 2)}{λ_{A} - λ_{B}} = \frac{6 \ln 2}{\frac{\ln 2}{5} - \frac{\ln 2}{30}} = \frac{6 \times 150}{25} = 36 days$

Watch 3-min video & get full concept clarity

JEE

NEET

Foundation JEE

Foundation NEET

CBSE