Question

A certain radioactive substance decays from 100000 grams to 1000 grams in 34 days. What's it's half-life ?

Answer 1

Half life of the radioactive element is 5 days.

Explanation:

Formula to get the final amount after the radioactive decay in 't' days,

`A_t=A_0e^(-\lambda t)`

Here
`A_0` = Initial amount

λ = Decay constant

t = duration of decay

`A_t` = Final amount

`1000=100000e^(-\lambda(34))`

0.01 =
`e^(-34\lambda)`

ln(0.01) =
`\text{ln}(-e^(34\lambda)})`

-4.6052 = -34λ

λ = 0.13544

Since, λ =
`\frac{\text{ln}(2)}{t_{(1)/(2)}}`

`t_{(1)/(2)}=\frac{\text{ln}2}{0.13544}`

= 5.11

≈ 5 days

Therefore, half life of the radioactive element is 5 days.