Question

What is the half life of an atom that goes from 16000 g to 125 g in 163.24 days.

Answer 1

`23.32\ \text{days}`

Step-by-step explanation:

N = Final mass of atom = 125 g

`N_0` = Initial mass of atom = 16000 g

t = Time taken = 163.24 days

`t_(1/2)` = Half life

We have the relation

`N=N_0(1)/(2)^{(t)/(t_(1/2))}\\\Rightarrow 125=16000* (1)/(2)^{(163.24)/(t_(1/2))}\\\Rightarrow (125)/(16000)=(1)/(2)^{(163.24)/(t_(1/2))}\\\Rightarrow \ln0.0078125=(163.24)/(t_(1/2))\ln0.5\\\Rightarrow t_(1/2)=(163.24*\ln0.5)/(\ln0.0078125)\\\Rightarrow t_(1/2)=23.32\ \text{days}`

The half life of the atom is
`23.32\ \text{days}`.