Understanding Half-Life and Probability of Nucleus Disintegration

Half-life is the time taken for half of the radioactive material to disintegrate. For instance, if a radioactive element has a half-life of 5 years, it means that after 5 years, half of the initial radioactive material would have decayed.

Probability of nucleus disintegration refers to the likelihood that a nucleus will decay within a given period. Probability is usually expressed as a fraction or decimal, ranging from 0 to 1.

Calculating Probability of Nucleus Disintegration

To calculate the probability of nucleus disintegration, we use the formula:

P = 1 - (1/2)^(t/h)

Where:
P = Probability of nucleus disintegration
t = Time period
h = Half-life

Using the given values:
t = 10 years
h = 5 years

P = 1 - (1/2)^(10/5)
P = 1 - (1/2)^2
P = 1 - (1/4)
P = 0.75

Therefore, the probability of nucleus disintegration during 10 years is 0.75 or 75%. This means that there is a 75% chance that the nucleus will decay within the given period.

Conclusion

In summary, the probability of nucleus disintegration is the likelihood that a nucleus will decay within a given period. The half-life of a radioactive material is used to calculate the probability of nucleus disintegration. Using the given values, we can calculate the probability by using the formula P = 1 - (1/2)^(t/h), where P is the probability, t is the time period, and h is the half-life.