Answer :
Answer:
d) 12800 years.
Step-by-step explanation:
The equation for the decay of radioactive material has the following form:
[tex]m (t) = m_{o}\cdot e^{-\frac{t}{\tau} }[/tex]
[tex]\frac{m(t)}{m_{o}} = \exp(-\frac{t}{\tau} )[/tex]
Where [tex]\tau[/tex] is the time constant.
There is a relation between half-life and time constant:
[tex]\tau = \frac{t_{1/2}}{\ln 2} \\\tau = \frac{6230 yr}{\ln 2}\\\tau = 8987.99 yr[/tex]
The estimated age of the sample is isolated from the decay equation:
[tex]t = - \tau \cdot \ln \frac{m(t)}{m_{o}} \\t = - (8987.99 yr) \cdot \ln 0.24\\t \approx 12826.908 yr[/tex]
The correct answer is D.
The age of the sample is estimated to be option d. 12,800 years.
Calculation of the age of the sample:
Since The amount of a radioactive material has been reduced to 24 percent of the original value and the half-life is 6230 years.
So,
We have to know the relation first between the half-life and time constant
[tex]= 6230 \div ln2[/tex]
= 8987.99 year
Now the estimated age is
= -8987.99 year (ln0.24)
= 12,800 years
Hence, we can conclude that The age of the sample is estimated to be option d. 12,800 years.
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