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The half-life of a radioactive sample undergoing α-decay is 1.4 × 1017 sec. If the number of nuclei in the sample is 2.0 × 1021, the activity of the sample is nearly equal to: [2021]
- a)104 Bq
- b)105 Bq
- c)106 Bq
- d)103 Bq
Correct answer is option 'A'. Can you explain this answer?
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Understanding the Problem:
The problem provides information about the half-life of a radioactive sample undergoing α-decay and the initial number of nuclei in the sample. We need to calculate the activity of the sample.
Calculating Activity:
Given:
Half-life (t1/2) = 1.4 x 10^17 sec
Number of nuclei (N) = 2.0 x 10^21
The decay constant (λ) can be calculated using the formula:
λ = 0.693 / t1/2
Substitute the values:
λ = 0.693 / 1.4 x 10^17
λ ≈ 4.95 x 10^-18 s^-1
Activity (A) is given by:
A = λ * N
Substitute the values:
A ≈ 4.95 x 10^-18 * 2.0 x 10^21
A ≈ 9.9 x 10^3 s^-1
Converting s^-1 to Bq (Becquerel):
1 Bq = 1 s^-1
Therefore, the activity of the sample is approximately 10^4 Bq, which corresponds to option 'A'.
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The half-life of a radioactive sample undergoingα-decay is 1.4 × 1017sec.If the number of nuclei in the sample is 2.0× 1021,the activity of the sampleis nearly equal to: [2021]a)104 Bqb)105 Bqc)106 Bqd)103 BqCorrect answer is option 'A'. Can you explain this answer?
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