Question

Radium-226 is a radioactive substance with an annual decay rate of 0.04 % . A series of coal mines in Poland contain an abundance of the aforementioned isotope of radium. If these coal mines contained 400 thousand kilograms of radium-226 in 1937, then how much radium-226 would be left in those coal mines in 2017? Round your answer to the nearest kilogram.

Answer 1

i.e. 393650 kg.

Explanation:

Given that Radium-226 is a radioactive substance with an annual decay rate of 0.04 %

Let the year 1937 be 0 year

Initially population was = 400,000 kg

Since decay rate is 0.04% per year after t years population would be

`P(t) = 400,000 (1-0.0004)^t`

=
`400,000*0.9996^t`

In 2017, t = 40 years (i.e. years lapsed form 1937)

Hence population

=
`P(40) = 400,000 (0.9996)^(40) \\=393649.66`

i.e. 393650 kg.