Question

A wooden piece is $11520$ years old.

What is the fraction of $C^{14}$ activity left in the piece?

• A. $0.25$
• B. $0.5$
• C. $0.65$
• D. $0.35$

Answer 1

The correct option is A $0.25$

As we know,
$k=\frac{2.303}{t}log\left(\frac{N_0}{N}\right)$
or, $\frac{0.693}{t_{1/2}}=\frac{2.303}{t}log\left(\frac{N_0}{N}\right)[k=\frac{0.693}{t_{1/2}}]$
$\frac{0.693}{5760}=\frac{2.303}{11520}log\left(\frac{N_0}{N}\right)$
$\therefore \frac{N}{N_0}=0.25$