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ale4655 [162]
3 years ago
6

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

Chemistry
1 answer:
Alenkinab [10]3 years ago
3 0

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}.

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