Search any question & find its solution
Question:
Answered & Verified by Expert
A radioactive element $X$ converts into another stable element $Y$. Half life of $X$ is 2 hours. Initially only $X$ is present. After a time $t$, if the ratio of atoms of $X$ to $Y$ is $1: 4$, then the value of $t$ is
Options:
Solution:
1259 Upvotes
Verified Answer
The correct answer is:
between 4 hours and 6 hours
Initially at $t=0$, amount of $X$ in
sample $=5 X$
After time ' $t$ ' amount of $X$ remained in sample $=X$
From, $\frac{N}{N_0}=\left(\frac{1}{2}\right)^{\frac{t}{T}}$
We have, $\frac{X}{5 X}=\left(\frac{1}{2}\right)^{\frac{t}{2}} \Rightarrow\left(\frac{1}{2}\right)^{\frac{t}{2}}=\frac{1}{5}$
$\therefore T=2 \mathrm{~h}$
As, $\frac{1}{2^2} < \frac{1}{5} < \frac{1}{2^3} \Rightarrow \frac{1}{2^2} < \frac{1}{2^{t / 2}} < \frac{1}{2^3}$
$2 < t / 2 < 3 \Rightarrow 4 < t < 6$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.