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 ________ . [2023]

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Solution

Q.
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: $h = 6 \times 10^{- 34} Js,$ $m_{e} = 9 \times 10^{- 31} kg$ [2023]

(A) The de Broglie wavelength of the electron emitted is 666.67 nm.

(B) The characteristics 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.

Ans.
(2)

Given mass of electron $= 9 \times 10^{- 31} kg$ ,

$h = 6 \times 10^{- 34} J/sec$

$Wavelength (λ) = \frac{h}{m_{e} v_{e}} = \frac{6 \times 10^{- 34}}{9 \times 10^{- 31} \times 10^{3}}$

$= \frac{2}{3} \times 10^{- 6} m$

$= 0.66667 \times 10^{- 6} m$

$= 666.67 \times 10^{- 9} m$

$= 666.67 nm$

Cathode rays do not depend on the nature of the gas and metal plate.

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