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JEE Main 201816 AprilOnline

Exam: JEE Main
Year: 2018
Date: 16 April
Mode: Online
Subject: Physics
Chapter: Nuclear Physics

JEE Main 2018 · 16 April · Online · Physics · Nuclear Physics

At some instant, a radioactive sample S _ 1 having an activity 5...

At some instant, a radioactive sample

{S}_{1}

having an activity

5\muCi

has twice the number of nuclei as another sample

{S}_{2}

which has an activity of

10\muCi

. The ratio of half lives of

{S}_{1}and{S}_{2}

is

Options

A $4: 1$
B $1: 4$
C $1: 2$
D $2: 1$

Correct answer

A. $4: 1$

Step-by-step solution

Given:

{N}_{1} = 2.{N}_{2}

Now, activity

{A}_{1} = {\lambda}_{1}{N}_{1} = 5\mu{C}_{i} . . . . . ( 1 )

and

{A}_{2} = {\lambda}_{2}{N}_{2} = 10\mu{C}_{i} . . . . . ( 2 )

Dividing

\dfrac{( 1 )}{( 2 )}

we get

\dfrac{{\lambda}_{1}}{{\lambda}_{2}} . \dfrac{{N}_{1}}{{N}_{2}} = \dfrac{5}{10}

⇒ \dfrac{{t}_{2}}{{t}_{1}} .2 = \dfrac{1}{2} ⇒ \dfrac{{t}_{1}}{{t}_{2}} = \dfrac{4}{1}

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