Atoms And Nuclei Question 366
Question: A radioactive element X converts into another stable element Y. Half-life of X is 2 hrs. Initially only X is present. After time t, the ratio of atoms of X and Y is found to be 1 : 4, then t in hours is
Options:
A) 2
B) 4
C) between 4 and 6
D) 6
Show Answer
Answer:
Correct Answer: C
Solution:
-
Let $ N_{0} $ be the number of atoms of X at time $ t=0. $
Then at $ t=4 $ hrs (two half-lives) $ N_{x}=\frac{N_{0}}{4} $
and $ N_{y}=\frac{3N_{0}}{4} $
$ \therefore N_{x}/N_{y}=1/3 $and at $ t=6 $ hrs (three half-lives) $ N_{x}=\frac{N_{0}}{8} $
and $ N_{y}=\frac{7N_{0}}{8} $ or $ \frac{N_{x}}{N_{y}}=\frac{1}{7} $
The given ratio $ \frac{1}{4} $ lies between $ \frac{1}{3} $
and $ \frac{1}{7} $ .
Therefore, t lies between 4 hrs and 6 hrs.
