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The radioactivity of an old sample of whisky due to tritium (half-life 12.5 years) was found to be only about 4% of that measured in a recently purchased bottle marked 10 years old. The age of a sample is ______ years.

#### Options

60.00

65.00

68.00

70.00

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#### Solution

The radioactivity of an old sample of whisky due to tritium (half-life 12.5 years) was found to be only about 4% of that measured in a recently purchased bottle marked 10 years old. The age of the sample is **68.00** years.

**Explanation:**

`N_1 = N_0e^{-lambda.10}`

`N_2 = N_0e^{-lambdax}`

`N_2/N_1 = 4/100 = e^{lambda(10 - x)}`

`e^{lambda(x - 10)} = 100/4`

λ(x - 10) = 2 ln 10 - ln 4

λ(x - 10) = 2(2.3) - 2(0.693)

λ(x - 10) = 3.22

Now, `lambda = 0.693/12.5` yr^{-1}

∴ x - 10 = `12.5/0.693 xx 3.22`

= 58.08

x ≅ 68 years

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