Test Index

BITSAT 2016 Paper

Section: Physics

© examsnet.com

Question : 10 of 150

Marks: +1, -0

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

2
4
between 4 and 6
6

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} \text{ and } N_y = \frac{3N_0}{4}

\therefore \frac{N_x}{N_y}

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.

© examsnet.com

Go to Question:

Prev Question

Next Question