The half-life of a particular element is 280 days. what is its decay constant?

The formula for decay is

N' = Ne^ (-kt)

with N as the initial amount, k as the decay constant, and N' as the final amount. For decay, 280 days is the time it takes for the initial amount N to decay to 1/2N (half its original mass).

1/2A = Ae^ (-280k)

1/2 = e^ (-280k)

Solving for k, we will yield

ln (1/2) = - 280k

k = ln (2) / 280 day^-1

k ≈ 2.5 * 10^-3 day^-1