Question

If 10% of a radioactive substance decays in every 5 years, then the percentage of the substance that will have decayed in 20 years will be ______.

Options

• 40%

• 50%

• 65.6%

• 34.4%

Answer 1

If 10% of a radioactive substance decays in every 5 years, then the percentage of the substance that will have decayed in 20 years will be 34.4%.

Explanation:

`N_1/N_0 = 90%`

= 0.9 = `(1/2)^{5"/"T}`

`N_2/N_0 = (1/2)^{20"/"T} = (0.9)^4`

= 65.6% `N_d/N_0`

= `1 - N_2/N_0 = 34.4%`