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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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Question

The half-life of a certain radioactive nucleus is 3.2 days. Calculate (i) decay constant (ii) average life of radioactive nucleus.

Sum
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Solution

Given: T1/2 = 3.2 days

To find:

  1. decay constant (λ)
  2. average life (τ) 

Formulae:

  1. T1/2 = `0.693/lambda`
  2. `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

  1. The decay constant of reaction is 0.2166 /day.
  2. The mean life of the species is 4.617 days. 
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Chapter 15: Structure of Atoms and Nuclei - Short Answer I

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