Answer:
[tex]23.32\ \text{days}[/tex]
Explanation:
N = Final mass of atom = 125 g
[tex]N_0[/tex] = Initial mass of atom = 16000 g
t = Time taken = 163.24 days
[tex]t_{1/2}[/tex] = Half life
We have the relation
[tex]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}[/tex]
The half life of the atom is [tex]23.32\ \text{days}[/tex].
