Electrons in a cathode ray tube have been emitted with a velocity of 1000 m s⁻¹. The number of following statements which is/are true about the emitted radiation is ____________.
Given : h=6×10⁻³⁴ J s,mₑ=9×10⁻³¹ kg.
(A) The de-Broglie wavelength of the electron emitted is 666.67 nm.
(B) The characteristic of electrons emitted depend upon the material of the electrodes of the cathode ray tube.
(C) The cathode rays start from cathode and move towards anode.
(D) The nature of the emitted electrons depends on the nature of the gas present in cathode ray tube.

Solution

Chemistry ma’am · 3 steps

Do the one calculation for (A), then remember that cathode rays look the same whatever the gas or metal.

1. Check (A). Use the de Broglie relation λ = h/mv with m = 9 × 10⁻³¹ kg and v = 1000 m s⁻¹.

   λ = (6 × 10⁻³⁴)/(9 × 10⁻³¹ × 10³) = 6.667 × 10⁻⁷ m = 666.67 nm

2. Cathode ray facts. Cathode rays leave the cathode and travel towards the anode. Their charge-to-mass ratio is the same for every cathode material and every gas, because they are always electrons.

   Statement	Verdict	Reason
   (A)	True	λ works out to 666.67 nm
   (B)	False	Electrode material does not change the electrons
   (C)	True	They move from cathode to anode
   (D)	False	The gas inside the tube does not change the electrons

3. So. Only (A) and (C) are true, so the answer is 2.

The common slip: 3. Treating (B) or (D) as true gives 3. That mixes cathode rays up with anode rays, which are the ones that depend on the gas.

The idea to keep. Cathode rays do not depend on the gas or the electrode material. Anode (canal) rays do, because they are positive ions of the gas.

Answer from the NTA final answer key. Solution by PrepWiser.