57 Co decays to 57 Fe by -emission- The resulting 57 Fe is in its excited state and comes to the ground state by emitting -rays- The half-life of -decay is 270 days and that of the -emissions is 10-8 s- A sample of 57 Co 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-

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Byju's Answer

Standard XII

Biology

Exponential Growth Function

57 Co decays ...

Question

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?

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Solution

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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$^{57} Co$ decays to $^{57} Fe$ by $β^{+}$ emission. The resulting $^{57} Fe$ 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 $γ$ emission is $10^{- 6}$ s. A sample of $^{57} Co$ gives 5.0 $\times 10^{9}$ gamma rays per second. How much time will elapse before the emission rate of gamma rays drops to 2.5 $\times 10^{9}$