Question

A sample of a radioactive isotope of an element contains 60 million atoms and is found to have a decay rate of 8 hundred atoms per year. What is the half-life of the isotope? (Give your answer correct to at least two decimal places.)

Answer 1

Answer:

The half-life of the isotope is 3.75 × 10⁴ years.

Explanation:

Hi there!

The half-life of the radioactive isotope is the time at which half of the atoms of the sample decay.

The sample has 6.00 × 10⁷ atoms and every year 8.00 × 10² of them decay. Then, we have to find the time at which 30 million atoms decay:

If  8.00 × 10² atoms decay per year, 3.00 × 10⁷ atoms will decay in:

3.00 × 10⁷ atoms · ( 1 year / 8.00 × 10² atoms) = 3.75 × 10⁴ years

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