Question

The half-life of a radioactive element is 3 hours. If the initial mass of the isotope were 256 g, the mass of it remaining undecayed after 18 hours would be (in gm) _________.

Answer 1

since $t_{1/2}=\frac{0.693}{k}$
$⟹k=\frac{0.693}{3}$

Radioactive decay is first order reaction
$⟹\frac{0.693}{3}=\frac{2.303}{18}\log \frac{256}{x}$
$⟹\frac{6\times 0.693}{2.303}=\log \frac{256}{x}$
$⟹x=4gm$