JEE Main · 2022 · 28 Jun 2022 · Shift 2 · Modern Physics

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Following statements related to radioactivity are given below:
(A) Radioactivity is a random and spontaneous process and is dependent on physical and chemical conditions.
(B) The number of un-decayed nuclei in the radioactive sample decays exponentially with time.
(C) Slope of the graph of

lo g_{e}

(no. of undecayed nuclei) Vs. time represents the reciprocal of mean life time

(τ)

.
(D) Product of decay constant (

λ

) and half-life time (

T_{1/2}

) is not constant.

Choose the most appropriate answer from the options given below:

(A)(A) and (B) only
(B)(B) and (D) only
(C)(B) and (C) only✓ Correct
(D)(C) and (D) only

Answer: (C)

Solution

Let's analyze each statement:

(A) FALSE: Radioactivity is a random and spontaneous process but is INDEPENDENT of physical and chemical conditions.

(B) TRUE: The number of undecayed nuclei follows

N = N_{0} e^{- λ t}

, which is exponential decay.

(C) TRUE: From

N = N_{0} e^{- λ t}

, we get

ln N = ln N_{0} - λ t

. The slope of

ln N

vs.

t

- λ = - 1/ τ

(since mean lifetime

τ = 1/ λ

). So the slope represents the negative reciprocal of mean lifetime.

(D) FALSE: The product

λ T_{1/2} = ln 2 \approx 0.693

is a constant.

Therefore, statements (B) and (C) are correct.

JEE Main · 2022 · 28 Jun 2022 · Shift 2 · Single correct option

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JEE Main · 2022 · 28 Jun 2022 · Shift 2 · Modern Physics

Solution

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