Question

The half-life of ${}^{14}C$ is 5570 yr. How many years will it take 90% of a sample to decompose?

• A. 5,570 yr
• B. 17,700 yr
• C. 18,510 yr
• D. 50,100 yr

Answer 1

Answer: (C)

18,510 yr

The half-life of ${}^{14}C$ is $5570yr.$

$t_{1/2}=5570$ years

The decay constant $\lambda =\frac{0.693}{t_{1/2}}$

$\lambda =\frac{0.693}{5570yr}$

Also $t=\frac{2.303}{\lambda }log\left(\frac{a}{a-x}\right)$

$t=\frac{2.303}{\frac{0.693}{5570yr}}log\left(\frac{100}{100-90}\right)$

$t=18,510yr$

So, the correct option is $C$