The decay constant (λ) of a radioactive element can be calculated using the formula:
λ = ln(2) / T1/2
where ln(2) is the natural logarithm of 2 and T1/2 is the half-life of the element.
Substituting the given values, we get:
λ = ln(2) / (4 x 10^8)
λ = 1.73 x 10^-9 per year
Therefore, the decay constant of the radioactive element is 1.73 x 10^-9 per year.
The mean life (τ) of a radioactive element can be calculated using the formula:
τ = 1 / λ
Substituting the calculated value of λ, we get:
τ = 1 / (1.73 x 10^-9)
τ = 5.78 x 10^8 years
Therefore, the mean life of the radioactive element is 5.78 x 10^8 years.