JEE Main · 2019 · 09 Jan 2019 · Shift 1 · Modern Physics

A sample of radioactive material A , that has an activity of

10 mCi (1 Ci = 3.7 \times 1 0^{10}

decays/s), has twice the number of nuclei as another sample of different radioactive material B which has an activity of 20 mCi . The correct choices for half-lives of A and B would then be respectively:

(A)5 days and 10 days
(B)10 days and 40 days
(C)20 days and 5 days✓ Correct
(D)20 days and 10 days

Answer: (C)

Solution

Activity is

A = λ N

. For the two samples,

10 = λ_{A} N_{A}

and

20 = λ_{B} N_{B}

, with

N_{A} = 2 N_{B}

. Dividing,

\frac{10}{20} = \frac{λ _{A} ( 2 N _{B} )}{λ _{B} N _{B}}

, which gives

\frac{λ _{A}}{λ _{B}} = \frac{1}{4}

. Half-life runs inversely with

λ

, so

\frac{T _{A}}{T _{B}} = \frac{λ _{B}}{λ _{A}} = 4

; the pair

20

days and

5

days is the one standing in that

4 : 1

ratio.

JEE Main · 2019 · 09 Jan 2019 · Shift 1 · Single correct option

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JEE Main · 2019 · 09 Jan 2019 · Shift 1 · Modern Physics

Solution

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