Help to exercise 3

The last question of exercise 3 asks you to calculate how much there was of the irradiated metal. Per will lecture on this on Wednesday, I believe, so this problem might have been a little more challenging than I intended...

Therefore, here is a little help on this subject:

Yield in neutron irradiation and nuclear reactions

Chapter 8 in the textbook deals with nuclear reactions and you'll find what you need in sub-chapter 8.5: "Yield of Nuclear Reactions". Equation 8.27 is what you want:

where

• A is the activity of the produced nucleus B (which you calculate from your efficiency curve),
• lambda  is the half life of the product nucleus B,
• N_A is the number of atoms of the target nucleus (in the case of exercise 3 this is the amount of the unknown metal),
• sigma is the cross section (the likelihood of a reaction between the neutrons and the target nucleus A), and finally
• theta is the neutron flux (the number of neutrons hitting the target).

What this equation tells you is that if you irradiate N_A atoms of A (usually referred to as your "target") with neutrons of intensity theta for a time t, the disintegration rate of your product will be A (do not mix the target nucleus A with the activity, A, of the product nucleus B!).

You'll find sigma in the nuclear chart (it's around 20 for the unknown metal). It's unit is barn, which is equal to 10^-24 cm². The neutron flux is given in the exercise text and is equal to 10⁵ . When you multiply these two numbers you are left with s^-1, which is the correct unit for the disintegration rate.

Good luck!