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JJ Thomson did an experiment with discharge tube using hydrogen gas. Later it was found that anode rays and Cathode rays both exist at the same time.. Cathode rays move opposite to anode rays. My doubt is that if cathode rays and anode rays both exist at same time and are opposite to each other then why did the wheel rotate which was kept inside the tube since the wheel was experiencing force from both sides it should should rotate but how did it rotate. Edit: by 'later' i mean when anode rays were discovered.

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Actually anode rays are not emitted from anode and reaching cathode. It is produced it the middle of the tube. When high voltage is applied on electrodes the cathode emits electrons which collide with the residual gas knocking of electron from that gas molecule which travel towards the anode and the positively charged gaseous atom gaseous atom moves back to cathode which is anode rays.

However, the tube must be set up quite differently from the usual cathode ray set-up in order to detect canal (or anode) rays.

Cathode ray tube and Anode ray tube

So you should place it different tube to get the paddle wheel move by anode or cathode rays.

Then this is what i found in Wikipedia

Crookes put a tiny vaned turbine or paddlewheel in the path of the cathode rays, and found that it rotated when the rays hit it. The paddlewheel turned in a direction away from the cathode side of the tube, suggesting that the rays were coming from the cathode. Crookes concluded at the time that this showed that cathode rays had momentum, so the rays were likely matter particles. However, later it was concluded that the paddle wheel turned not due to the momentum of the particles (or electrons) hitting the paddle wheel but due to the radiometric effect (it is the repulsive force between two surfaces maintained at different temperatures). When the rays hit the paddle surface they heated it, and the heat caused the gas next to it to expand, pushing the paddle.

https://en.wikipedia.org/wiki/Crookes_tube#Paddlewheel

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the mass of the cathode rays are very small compared to positive ions (electron and positive ions are produce in the discharge tube). when why voltage is apply then the kinetic energy of electron is greater then positive ions because k.E= P2(momentum square)/2m . at same voltage when mass is increases then k.E will be decreases . then electron gain more momentum therefore to rotate the wheel.

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