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

To evaluate the truthfulness of the statements provided about the cathode rays, we will analyze each statement one by one:

(A) The deBroglie wavelength of the electron emitted is \(66667 \, \text{nm}\):
The deBroglie wavelength \(\lambda\) is calculated using the formula \(\lambda = \frac{h}{mv}\), where \(h\) is Planck's constant, \(m\) is mass of the electron, and \(v\) is its velocity.
Given: \(h = 6 \times 10^{-34} \, \text{Js}\), \(m = 9 \times 10^{-31} \, \text{kg}\), \(v = 1000 \, \text{m/s}\).
Plugging in these values, \(\lambda = \frac{6 \times 10^{-34}}{9 \times 10^{-31} \times 1000}\).
Calculating, \(\lambda = \frac{6 \times 10^{-34}}{9 \times 10^{-28}}\).
\(\lambda = \frac{2}{3} \times 10^{-6} \, \text{m} = \frac{2}{3} \times 10^{3} \, \text{nm} = 0.667 \, \text{nm}\).
Therefore, statement (A) is false.

(B) The characteristic of electrons emitted depend upon the material of the electrodes of the cathode ray tube:
This statement is true. The material of electrodes influences the characteristics such as work function which affects the emission of electrons.

(C) The cathode rays start from cathode and move towards anode:
This is correct and describes the basic principle of cathode ray tubes. Thus, statement (C) is true.

(D) The nature of the emitted electrons depends on the nature of the gas present in cathode ray tube:
This statement is false. The electrons in cathode rays are not influenced by the gas present; they are inherent to the materials and structure of the tube.

In conclusion, the true statements are (B) and (C), tallying to a total of 2. The computed value 2 falls within the expected range [2,2].