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, $t_{1/2} = 77 \text{ days}$

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

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