JEE Main · 2023 · 01 Feb 2023 · Shift 1 · Atomic Structure

Electrons in a cathode ray tube have been emitted with a velocity of

1000 ms^{- 1}

. The number of following statements which is/are true about the emitted radiation is ____.

Given :

h = 6 \times 1 0^{- 34} Js, m_{e} = 9 \times 1 0^{- 31} kg

.
(A) The deBroglie 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.

Answer: 2

Solution

The de Broglie wavelength of the emitted electrons is

λ = \frac{h}{m v} = \frac{6 \times 1 0 ^{- 34}}{( 9 \times 1 0 ^{- 31} ) ( 1000 )} = \frac{2}{3} \times 1 0^{- 6} m = 666.67 nm

, so that statement is correct. Cathode rays are produced at the cathode and travel towards the anode, which is also correct. Their properties, however, are simply those of electrons and are entirely independent of the material of the electrodes and of the gas filling the tube, so those two statements are wrong. The number of true statements is 2.

JEE Main · 2023 · 01 Feb 2023 · Shift 1 · Integer answer

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JEE Main · 2023 · 01 Feb 2023 · Shift 1 · Atomic Structure

Solution

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