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Question
The half-life of a certain radioactive nucleus is 3.2 days. Calculate (i) decay constant (ii) average life of radioactive nucleus.
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Solution
Given: T1/2 = 3.2 days
To find:
- decay constant (λ)
- average life (τ)
Formulae:
- T1/2 = `0.693/lambda`
- `tau = 1/lambda`
Calculation:
From formula (i),
3.2 = `0.693/lambda`
∴ `lambda = 0.693/3.2`
∴ λ = antilog {log(0.693) − log(3.2)}
= antilog {`overline1`.8407 − 0.5051}
= antilog {`overline1`.3356}
= 0.2166 /day
From formula (ii),
`tau = 1/0.2166`
Using reciprocal table,
`tau` = 4.617 days
- The decay constant of reaction is 0.2166 /day.
- The mean life of the species is 4.617 days.
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