If the half-life of a substance is $77 ext{ days}$ then its decay constant ($ ext{days}^{-1}$) will be:

Question

If the half-life of a substance is $77 	ext{ days}$ then its decay constant ($	ext{days}^{-1}$) will be:

Accepted Answer

Radioactive decay follows first-order kinetics. The decay constant ($k$ or $\lambda$) is related to the half-life ($t_{1/2}$) by the relation:

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

Given:
Half-life, $t_{1/2} = 77 	ext{ days}$

Substituting the given value:
$k = \frac{0.693}{77 	ext{ days}} = 0.009 	ext{ days}^{-1}$.

Therefore, the decay constant is $0.009 	ext{ days}^{-1}$.