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 × 109per second?

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+- - Physics

Sum

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 × 10⁹per second?

Advertisement Remove all ads

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.

Concept: Radioactivity - Law of Radioactive Decay

Is there an error in this question or solution?

Chapter 24: The Nucleus [Page 443]

Q 28 Q 27 Q 29

Advertisement Remove all ads