Question

Element X decays radioactively with a half life of 6 minutes. If there are 970 grams of

Element X, how long, to the nearest tenth of a minute, would it take the element to
decay to 139 grams?
y = a(.5) *

Answer 1

Answer: 16.81 min

Explanation:

Given

Initial concentration
`A_o=970\ gm`

Half-time
`T_{(1)/(2)}=6\ min`

Decay at any time t is given by

`A=A_o2^{\frac{-t}{T_{(1)/(2)}}}`

put values

`\Rightarrow 139=970\cdot 2^{(-t)/(6)}\\\\\Rightarrow 2^{(t)/(6)}=6.978\\`

Taking log both sides

`\Rightarrow (t)/(6)* \ln (2)=\ln (6.978)\\\\\Rightarrow t=6* 2.802\\\Rightarrow t=16.81\ \text{min}`