araz said:A radioactive source emits particles at an average rate of 1 pe second. Assume that the number of emissions follows a Poisson distribution. The emission rate changes such that the probability of 0 or 1 emission in 4 seconds becomes 0.8. What is the new rate? Thanks.
Klaas van Aarsen said:Hi araz, welcome to MHB! ;)
We have:
$$P(\text{0 or 1 emission in 4 seconds})=0.8 \\ \implies
P(\text{0 emission in 4 seconds}) + P(\text{1 emission in 4 seconds}) = \frac{\lambda^0 e^{-\lambda}}{0!} + \frac{\lambda^1 e^{-\lambda}}{1!} = (1+\lambda)e^{-\lambda} = 0.8 \\ \implies
\lambda \approx 0.824
$$
So the average number of emissions in 4 seconds is $0.824$, which is $0.206$ per second.
araz said:Thank you Klaas. Did you use guess and check or numerical methods to get 0.824?
Regards
The formula for calculating the new emission rate of a radioactive source is: New Emission Rate = Initial Emission Rate x (Current Half-life / New Half-life)^2.
The current half-life of a radioactive source can be determined by measuring the amount of time it takes for half of the radioactive material to decay. This can be done through various methods such as counting the number of decays per second or measuring the intensity of the radiation emitted.
The accuracy of the calculated emission rate can be affected by factors such as measurement errors, changes in the physical environment of the radioactive source, and the presence of other radioactive materials that may interfere with the decay process.
Yes, the emission rate of a radioactive source can change over time due to factors such as decay and changes in the physical environment. This is why it is important to regularly recalculate the emission rate to ensure accurate results.
The emission rate of a radioactive source is typically measured in units of becquerels (Bq) or curies (Ci). These units represent the number of decays per second or the amount of radioactive material present in a sample.