Question

why do cathode rays not depend on nature of gas and anode rays do?

Answer 1

Cathode rays are nothing but beams of electrons, all of which are identical so the charge to mass ratio (e/m) of cathode rays is same for all gases i.e. cathode rays do not depend on nature of gas.

Whereas, anode rays are composed of ionised nuclei which differ from gas to gas in terms of atomic & mass numbers. When the gas is changed, the e/m ratio of the positively charged ions obviously changes because the number of neutrons in the nucleus of each gas can be different (hydrogen has zero) and the number of protons in one nucleus of each gas is also different.