Question

In 8,450 seconds, the number of radioactive nuclei decreases to 1/16 of the number present initially. What is the half-life (in s) of the material

Answer 1

2113 seconds

Step-by-step explanation:

The general decay equation is given as
`N = N_0e^(-\lambda t) \\\\`, then;

`(N)/(N_0) = e^(-\lambda t) \\` where;

`N/N_0` is the fraction of the radioactive substance present = 1/16

`\lambda` 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;

`(1)/(16) = e^(-\lambda(8450)) \\\\Taking\ ln\ of \both \ sides\\\\ln((1)/(16) ) = ln(e^(-\lambda(8450))) \\\\\\ln ((1)/(16) ) = -8450 \lambda\\\\\lambda = (-2.7726)/(-8450)\\ \\\lambda = 0.000328`

Half life f the material is expressed as
`t_(1/2) = (0.693)/(\lambda)`

`t_(1/2) = (0.693)/(0.000328)`

`t_(1/2) = 2,112.8 secs`

Hence, the half life of the material is approximately 2113 seconds