The curve to the right shows the radioactive decay of a particular sample of a nucleus called Element A

The expression for the disintegration equation is given below:

 …… (1)

Half-life of the particle for  is as follows:

Substitute  for  in Equation (1).

Half-life of the particle for  is as follows:

Rearrange to find the fraction of the sample remains after some time of disintegration.

The probability to disintegrate is as follows:

Substitute  for  and  for .

The probability of an element decay between  to is .

Explanation | Common mistakes | Hint for next step

The rate of disintegration is always directly proportional to the amount of sample present at that time.

Step 2 of 2

The expression for the disintegration equation is given below:

Half-life of the particle for  is as follows:

Substitute  for  in Equation (1).

The probability to disintegrate is as follows:

Substitute  for  and  for .

The probability of an element decay between  to is .

Explanation | Common mistakes

The ratio of the number of favorable outcomes to a certain event and the total number of possible outcomes are defined as the probability of an event.

Answer

The probability of an element decay between  to is .

The probability of an element decay between  to is .