Qstnid -Iv-28-57co Decays To 57fe By Β+- Emission. The Resulting 57fe Is In Its Excited State And Comes To The Ground State By Emitting Γ-rays. The Half-life Of Β+- Decay Is 270 Days And That Of The Γ-emissions Is 10-8 S. A Sample Of 57co Gives 5.0 &Times; 109 Gamma Rays Per Second. How Much Time Will Elapse Before The Emission Rate Of Gamma Rays Drops To 2.5 &Times; 109 Per Second? - 46: The Nucleus

with Solutions - page 7

#28
⁵⁷Co decays to ⁵⁷Fe by β⁺- emission. The resulting ⁵⁷Fe is in its excited state and comes to the ground state by emitting γ-rays. The half-life of β⁺- decay is 270 days and that of the γ-emissions is 10^-8 s. A sample of ⁵⁷Co gives 5.0 × 10⁹ gamma rays per second. How much time will elapse before the emission rate of gamma rays drops to 2.5 × 10⁹ per second?
Ans : According to the question, when the β⁺ decays to half of its original amount, the emission rate of γ-rays will drop to half. For this, the sample will take 270 days.
Therefore, the required time is 270 days.
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