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The half-life of a radioactive sample undergoing α-decay is 1.4×10¹⁷ s. If the number of nuclei in the sample is 2.0×10²¹, the activity of the sample is nearly

Asked in NEET (Oct.) 2020 · Activity and decay constant

• (1) 10⁴ Bq
• (2) 10⁵ Bq
• (3) 10⁶ Bq
• (4) 10³ Bq

Step-by-step solution

Why the other options are wrong

• (2) comes from a decade high: N/T_1/2 alone is only 1.4×10⁴, and the factor 0.693 pulls the answer down, not up.
• (3) comes from two decades high: with N~10²¹ and T_1/2~10¹⁷ s the activity cannot reach 10⁶ Bq.
• (4) comes from a decade low: it would need a decay constant about ten times smaller than 0.693/T_1/2.

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