Mean Life Calculation of a Radioactive Sample

What is the mean life of a radioactive sample with a half-life of 4 seconds?

A) 0.25s

B) 1.44s

C) 6.17s

D) 5.8s

Answer:

The mean life of a radioactive sample with a half-life of 4 seconds can be calculated using the equation τ = T/ln(2), producing a value of approximately 5.77 seconds. Therefore, none of the provided options are precisely correct, but the closest is D) 5.8s.

The half-life of a substance can be used to find the mean life (also known as the average lifetime) of a radioactive sample. Given that the half-life (T) of your radioactive sample is 4 seconds, you use the relationship between half-life and mean life, which states that mean life (τ) is equal to the half-life divided by the natural logarithm of 2, or τ = T/ln(2).

In this scenario, the mean life would be calculated as 4s divided by 0.693 (approximate value of ln(2)), which equals approximately 5.77s. So, none of the options given appears to be correct. However, the closest value is D) 5.8s, which may be the intended answer depending on the approximation.