Nuclear reaction cross section

[thenewbosco]

Suppose we consider a beam of neutrons incident upon a thin target with an intensity of 10^12 neutrons/(cm^2.s). Suppose further that the total cross section for the nuclei in this target is 4 b. Using this information, determine how long one would have to wait, on the average, for a given nucleus in the target to suffer a neutron interaction.


The way i approached this is to get a rate from Intensity*cross section = rate
this gives

10^12 neutrons/(cm^2 sec) * 4.0 × 10^-24 cm^2 = 4 × 10-12 s^-1

Then taking 1/rate should give the length of time...but this gives an extraordinarily long time of course which leads me to believe something is wrong?
how should this be approached

 

[Jhero]

?

Thank you for your question. Your approach is correct, but there are a few things to consider in order to get a more realistic answer.

First, the intensity of 10^12 neutrons/(cm^2.s) is quite high, and it is more common to use a lower intensity in neutron experiments. This is because high intensity beams can cause damage to the target material and can also lead to multiple interactions occurring at the same time, making it difficult to determine the exact interaction time for a single nucleus.

Second, the cross section for neutron interactions can vary depending on the energy of the neutrons and the specific target material. So, the value of 4 b may not be accurate for all situations.

With that being said, let's assume that the intensity and cross section given in the question are accurate for our scenario. As you correctly calculated, the rate of neutron interactions would be 4 × 10^-12 s^-1. This means that on average, one interaction would occur every 1/(4 × 10^-12) = 2.5 × 10^11 seconds, or approximately 7.9 years. This is a long time, but as mentioned before, it is due to the high intensity and simplified assumptions used.

In reality, the interaction time for a given nucleus would depend on many factors, such as the specific energy and direction of the neutron, the location and orientation of the nucleus in the target, and the properties of the target material. These factors can be taken into account through more advanced calculations and simulations.

I hope this helps clarify the concept of interaction time for a given nucleus in a neutron beam. Keep in mind that the actual time may vary depending on the specific experimental conditions. Thank you for your question and happy experimenting!