Answer:
Explanation:
The general decay equation is given as [tex]N = N_0e^{-\lambda t} \\\\[/tex], then;
[tex]\dfrac{N}{N_0} = e^{-\lambda t} \\[/tex] where;
[tex]N/N_0[/tex] is the fraction of the radioactive substance present = 1/16
[tex]\lambda[/tex] is the decay constant
t is the time taken for decay to occur = 8,450s
Before we can find the half life of the material, we need to get the decay constant first.
Substituting the given values into the formula above, we will have;
[tex]\frac{1}{16} = e^{-\lambda(8450)} \\\\Taking\ ln\ of \both \ sides\\\\ln(\frac{1}{16} ) = ln(e^{-\lambda(8450)}) \\\\\\ln (\frac{1}{16} ) = -8450 \lambda\\\\\lambda = \frac{-2.7726}{-8450}\\ \\\lambda = 0.000328[/tex]
Half life f the material is expressed as [tex]t_{1/2} = \frac{0.693}{\lambda}[/tex]
[tex]t_{1/2} = \frac{0.693}{0.000328}[/tex]
[tex]t_{1/2} = 2,112.8 secs[/tex]
Hence, the half life of the material is approximately 2113 seconds
