SATHEE: Atoms And Nuclei Question 366

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 $N_{y} = \frac{3 N_{0}}{4}$
$∴ N_{x} / N_{y} = 1 / 3$

and at $t = 6$ hrs (three half-lives) $N_{x} = \frac{N_{0}}{8}$

and $N_{y} = \frac{7 N_{0}}{8}$ 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.

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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:

Answer:

Solution:

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