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A radioactive element X converts into another stable element Y

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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 :

between 4 and 6

Views: 5,847 students

Updated on: Feb 21, 2024

Book:

Physics Galaxy Optics and Modern Physics Vol 4 (Ashish Arora)

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Lucas Discussed

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 :

9 mins ago

Discuss this question LIVE

9 mins ago

Text solutionVerified

We use

N = N_{0} (2)^{- t / T}

so after time

t

we have

\frac{N _{0}}{5} = N_{0} (2)^{- t /2}

\Rightarrow t = 2 \frac{l o g 5}{l o g 2} = 4.64 hrs .

Let

N_{2}

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}

\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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Question Text	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 :
Updated On	Feb 21, 2024
Topic	Nuclei
Subject	Physics
Class	Class 12
Answer Type	Text solution:1 Video solution: 3
Upvotes	423
Avg. Video Duration	6 min

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 :

Text solutionVerified

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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 :

Text solutionVerified

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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 :