Question

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

Answer 1

Answer:

$23.32\ \text{days}$

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

$N=N_0\dfrac{1}{2}^{\dfrac{t}{t_{1/2}}}\\\Rightarrow 125=16000\times \dfrac{1}{2}^{\dfrac{163.24}{t_{1/2}}}\\\Rightarrow \dfrac{125}{16000}=\dfrac{1}{2}^{\dfrac{163.24}{t_{1/2}}}\\\Rightarrow \ln0.0078125=\dfrac{163.24}{t_{1/2}}\ln0.5\\\Rightarrow t_{1/2}=\dfrac{163.24\times\ln0.5}{\ln0.0078125}\\\Rightarrow t_{1/2}=23.32\ \text{days}$

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