I'm trying to understand if I could capture the event of generation of an electron positron pair from a gamma ray inside a cloud chamber. So far I've been thinking of using a cathode ray tube as a source of x-rays, since I have no idea on how I could find some x-ray radioactive sources themselves. The minimum energy of the x-ray emitted should be at least equal to the sum of the energy of the electron and positron at rest:
$$ E_\gamma^{(min)} = 2m_e c^2 = 1.023 MeV$$
Now I would like to capture the electron and positron curling inside the cloud chamber. So, as it is said in this thread, I assume that the gamma ray should be able to transfer some of its energy as momentum for the electron and positron. So the previous formula should become:
$$ E_\gamma = \sqrt{(2pc)^2 + (2m_ec^2)^2}= 2c\sqrt{p^2 + (m_ec)^2}$$
I assume that an energy of $1.1 - 1.5 MeV$ should be ok, but it is an estimate. Now the issue is, I can't understand how to calculate the medium energy of the x-rays produced by the cathode ray, given the pressure inside it, the voltage applied at the electrodes and the material of the electrodes.
So the question is, how could I determine the medium energy of the x-ray emitted? Moreover, is this method even feasible? (the next thing I was planning was just to place the cathode ray tube near the cloud chamber and hope for the event to happen, but I understand that it is a pretty clumsy solution) Are there other methods that are doable for an hobbyist at home?
P.S.: Thank you a lot in advance for any eventual answer; excuse my English, as I'm still learning it!
