Solved Numerical Problem No.3 ( Unit-20:Nuclear Physics); HSSC-II (Class-12); Physics (New Book/KPK Text Board, Peshawar) With Verified Answers

The half-life of radioactive nucleus `\ _{86}^{226}Ra` is 1.6 ｘ10³ years. Determine the decay constant. (Answer: 1.4 ｘ 10⁻¹¹ s⁻¹)

Given Data:

half life of radioactive nucleus `\ _{86}^{226}Ra` = `\T_{1∕2}` = 1.6 ｘ10³ years

by converting into Sec (SI unit) we have 1 year = 3.1536 ｘ10⁷ s  

`\T_{1∕2}` = 1.6 ｘ10³ ｘ 3.1536 ｘ10⁷ s = 5.0475 ｘ 10¹⁰ s

To Find:

The decay constant = λ =?

Solution:

Using the formula for Half-life we have

`\T_{1∕2}` = `\frac {0.693}{λ}`

or

 λ = `\frac {0.693}{T_{1∕2}}`

Putting values

 λ = `\frac {0.693}{5.0475 ｘ 10¹⁰ s}`

 λ = 0.1374 ｘ 10⁻¹⁰ s⁻¹

or

 λ = 1.374 ｘ 10⁻¹¹ s⁻¹ ----------------Ans.

Similar Questions:

The half-life of’ `\ _{38}^{91}Sr` is 9.70 hours. Find its decay constant. (Ans: 1.99 ｘ 10⁻⁵ s)

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