The decay constant for a radioactive isotope is 7.82 x 10-6 /y. What is the half-life of this isotope in years?

k = 0.693/t1/2

To find the half-life of a radioactive isotope, we can use the decay constant (denoted by λ). The decay constant is defined as the fraction of the remaining radioactive atoms that decay per unit time.

The formula relating the decay constant (λ) and the half-life (T½) is:
λ = ln(2) / T½

We are given the decay constant (λ) as 7.82 x 10^-6 /y. Therefore, we can rearrange the formula to solve for the half-life (T½):
T½ = ln(2) / λ

Now we can substitute the given decay constant (λ) to get the value of the half-life (T½):
T½ = ln(2) / (7.82 x 10^-6 /y)

Calculating this expression gives us the half-life of the isotope in years.