Question

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 : \(h =6 \times 10^{-34} J s , m _e=9 \times 10^{-31} kg\) 
(A) The deBroglie wavelength of the electron emitted is \(66667 nm\)
(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

Hint:

The de Broglie wavelength of a particle is inversely proportional to its momen tum (p = mv), and it helps describe wave-particle duality

Answer 1

Correct Answer: 2

Analysis of Statements:

1. Statement (A): The de Broglie wavelength (λ) is calculated using the formula:
   λ = h / mv
   Substituting the given values:
   \(λ = \frac{(6 × 10−34) }{ (9 × 10−31 × 1000)}\)
   λ = 6.67 × 10⁻⁷ m = 666.67 nm.
   This statement is true.
2. Statement (B): The emission of electrons in a cathode ray tube depends on the material of the cathode, as the work function and the energy required to emit electrons vary with the material.
   This statement is true.
3. Statement (C): Cathode rays are streams of electrons that start from the cathode (negative electrode) and travel towards the anode (positive electrode) in a cathode ray tube.
   This statement is true.
4. Statement (D): The electrons themselves are not affected by the nature of the gas present in the cathode ray tube. The nature of the gas may affect the fluorescence or color of the emitted light, but not the nature of the electrons.
   This statement is false.

Conclusion: The number of true statements is 2 (A and B).

Answer 2

The correct answer is 2.
(A) $V_c=1000m/s;h=6\times 10^{-34}Js$;
$m_e=9\times 10^{-31}kg$
$\lambda =\frac{h}{mv}=\frac{6\times 10^{-34}}{9\times 10^{-31}\times 1000}=666.67\times 10^{-9}m$
$=666.67nm$
(B) The characteristic of electrons emitted is independent of 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 is independent on the nature of the gas present in cathode ray tube.