What is the half-life period of a radioactive material if its activity drops to 1/16th of its initial value of 30 years? - Physics

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MCQ

What is the half-life period of a radioactive material if its activity drops to 1/16th of its initial value of 30 years?

Options

  • 9.5 years

  • 8.5 years

  • 7.5 years

  • 10.5 years

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Solution

7.5 years

Explanation:

The activity is given as,

A = Ao e-λt

⇒ -λt = ln `("A"/"A"_"o")`

⇒ `ln 2/"t"_(1//2)xx30=ln(1/16)`

⇒ `ln 2/"t"_(1//2)xx30=(ln2)xx-4`

⇒ t1/2 = `30/4`

= 7.5 years 

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