Question

The half-life of $C^{14}$ radioactive is 5760 yr. After how much time will 200 mg $C^{14}$ sample be reduced to 25 mg?

• A. 23040 yr
• B. 17280yr
• C. 11520 yr
• D. 5760 yr

Answer 1

Answer: (B)

$t_{1/2}=5760yr$
$N=N_0{\left(\frac{1}{2}\right)}^n$
$25=200{\left(\frac{1}{2}\right)}^n$
$\frac{25}{200}={\left(\frac{1}{2}\right)}^n$
$\frac{1}{8}={\left(\frac{1}{2}\right)}^n$
${\left(\frac{1}{2}\right)}^3={\left(\frac{1}{2}\right)}^n$
$n=3$ $=3\times 5760yr$
$=17280yr$