Question

A sample of a radioactive isotope of an element contains 50 million atoms and is found to have a decay rate of 5 hundred atoms per year. What is the half-life of the isotope? (Give your answer correct to at least two decimal places.)

Answer 1

Solution:-

Activity = λ N

and, t½ = 0.693 / λ

Where, λ = decay constant

N = Number of atoms in the sample.

t½ = half-life

Activity (or Decay rate) = 500 atoms / year

N = 50 million atoms = 5 × 10⁷ atoms

Thus,

(500 atoms / year) = λ . (5 × 10⁷ atoms)

or, λ = (500 atoms /year) / (5 × 10⁷ atoms)

or, λ = 1 × 10^-5 year^-1

Now,

t½ = (0.693) / (1 × 10^-5) = 69300 years

Hence, half-life of the isotope = 69300 years.

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