The half-life of a radioisotope is 20 years. Thus, the correct option is C.
What is Half-life?
Half-life may be defined as the duration carried for the radioactivity of a specified isotope to drop to half its original value.
The explanation for this question is as follows:
First, we have to calculate the rate constant.
Expression for rate law for first-order kinetics is given by:
[tex]k= \frac{2.303}{t} log \frac{a}{a-x}[/tex]
where,
k = rate constant = ?
t = time passed by the sample = 20 years
a = initial amount of the reactant = 100 g
a - x = amount left after decay process = 50 g.
Now put all the given values in the above equation, and we get,
[tex]k= \frac{2.303}{20} log\frac{100}{50}[/tex]
k= 0.0346/year.
Now we have to calculate the half-life, we use the formula :
[tex]k= \frac{0.693}{t_1_/_2}[/tex]
[tex]t_1_/_2[/tex] = [tex]\frac{0.693}{0.0346}[/tex]
[tex]t_1_/_2[/tex] = 20 years.
Therefore, it is well described above.
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