A Sample of radioactive material A, that has an activity of 10mCi (1Ci = 3.7 × 10 ^ 10 decays s ^ - 1 ), has twice the number of nuclei as another sample of a different radioactive material B which has an activity of

Correct answer: D. 20 days and 5 days Activity A = 10 = λ _ A N _ A 20 = λ _ B N _ B (1)/(2) = λ _ A λ _ B 2 λ _ A λ _ B = (1)/(4) ⇒ T _ A T _ B = (4)/(1)

JEE Main 20199 JanuaryMorning Shift

Exam: JEE Main
Year: 2019
Date: 9 January
Shift: Morning Shift
Subject: Physics
Chapter: Nuclear Physics

JEE Main 2019 · 9 January · Morning Shift · Physics · Nuclear Physics

A Sample of radioactive material A, that has an activity of 10mCi...

A Sample of radioactive material

A,

that has an activity of

10mCi

\left(1Ci = 3.7 \times {10}^{10}decays{s}^{- 1}\right),

has twice the number of nuclei as another sample of a different radioactive material

which has an activity of

20mCi

. The correct choices for half-lives of

A and

B

would then be, respectively:

Options

A $5$ days and $10$ days
B $10$ days and $40$ days
C $20$ days and $10$ days
D $20$ days and $5$ days

Correct answer

D. $20$ days and $5$ days

Step-by-step solution

Activity

A = \lambdaN

10 = {\lambda}_{A}{N}_{A}

20 = {\lambda}_{B}{N}_{B}

\dfrac{1}{2} = \dfrac{{\lambda}_{A}}{{\lambda}_{B}}2

\dfrac{{\lambda}_{A}}{{\lambda}_{B}} = \dfrac{1}{4} ⇒ \dfrac{{T}_{A}}{{T}_{B}} = \dfrac{4}{1}

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