A radioactive element has a decay constant of 0.077s-1, calculate its half life
Answer Details
The decay constant (λ) of a radioactive element is defined as the probability of decay of an individual nucleus per unit time. It can be mathematically shown that the number of nuclei (N) of a radioactive element remaining after time (t) is given by: N = N0 e-λt where N0 is the initial number of nuclei. The half-life of a radioactive element is the time taken for half of the radioactive nuclei to decay. Therefore, when N = 1/2 N0, we can rearrange the above equation to obtain the half-life (t1/2): t1/2 = ln2/λ Substituting the given value of the decay constant, we get: t1/2 = ln2/0.077 s-1 ≈ 9.0 s Therefore, the half-life of the radioactive element is approximately 9.0 s. Answer: 9.0s