Question :(a) How will the De Broghe wavelength associate with an electron he affected when the (i) velocity of the electron decreases? and
(ii) accelerating potential is increased? Justify your answer
The correct answer is -(a)(i) According to the de Broglie wavelength formula, the wavelength is inversely proportional to the momentum of the electron. As momentum is the product of mass and velocity, when the velocity of the electron decreases, its momentum also decreases. Therefore, the de Broglie wavelength of the electron will increase.
(a)(ii) When the accelerating potential is increased, the velocity of the electron also increases. As a result, the momentum of the electron increases, and according to the de Broglie wavelength formula, the wavelength decreases. Therefore, the de Broglie wavelength of the electron will decrease.
Justification: The de Broglie wavelength is given by λ = h/p, where h is Planck’s constant and p is the momentum of the particle. From the formula, it is evident that if the velocity of the electron decreases, the momentum of the electron also decreases, resulting in an increase in the de Broglie wavelength. Similarly, if the accelerating potential is increased, the velocity of the electron increases, leading to an increase in the momentum of the electron and a decrease in the de Broglie wavelength.
