Question

Suppose there are ten atoms, each of which decays by emission of an alpha particle after an exponentially distributed lifetime with rate λ, independently of the others. Let T1 be the time of the first alpha particle emission; T2 the time of the second. Find:

the distribution of T1;

Answer 1

The distribution of T1, the time of the first alpha particle emission, can be modeled using an exponential distribution with parameter λ. The PDF of T1 is given by f(t) = λe^(-λt), where λ is the decay rate and t is the time interval.

Step-by-step explanation:

The distribution of T1, which is the time of the first alpha particle emission, can be modeled by an exponential distribution with parameter λ. The exponential distribution represents the probability density function (PDF) of the time between events in a Poisson process, such as radioactive decay.

Let's denote T1 as the time of the first decay event. Then, the PDF of T1 is given by:

f(t) = λe^(-λt)

where λ is the decay rate (also known as the decay constant) and t is the time interval.