Question

The half life of $C^{14}$ is $5760$ years. For a "$200$" mg sample of $C^{14}$, the time taken to change to $25$ mg is __________ .

• A. $11520$ years
• B. $23040$ years
• C. $5760$ years
• D. $17280$ years

Answer 1

The correct option is D $17280$ years

Note: changing $200mg$ of $C^{14}$ to $25mg$ of $C^{14}$ is $\frac{1}{8}th$ times decrease in mass.

This means $3$ half-lives is needed.

Thus, $t=3\times t_{1/2}=3\times 5760=17280years$