Question

If the radioactive half-life of a substance is 20 days, and there are 5 grams of it initially. When will the amount left be 2 grams? Round to the nearest tenth of a day.

Answer 1

Answer:
`26.4\ \text{days}`

Explanation:

Given

Half life of radioactive substance is
`T_{(1)/(2)}=20\ \text{days}`

Initial amount
`A_o=2\ \text{days}`

Amount left at any time is given by

`\Rightarrow A=A_o2^{\frac{-t}{T_{(1)/(2)}}}\\\\\Rightarrow 2=52^{(-t)/(20)}\\\\\Rightarrow 0.4=2^{(-t)/(20)}\\\\\Rightarrow 2^{(t)/(20)}=2.5\\\\\Rightarrow (t)/(20)\ln 2=\ln (2.5)\\\\\Rightarrow t=(20\ln (2.5))/(\ln 2)\\\\\Rightarrow t=26.4\ \text{days}`

It takes 26.4 days to reach 2 gm.