Question

According to de Broglie, which of the following statements is true about the wavelength of a moving particle?
(a) It is never large enough to measure.
(b) It is proportional to the speed of the particle.
(c) It is inversely proportional to the momentum of the particle.
(d) it is equal to Planck’s constant
(e) it does not affect the behaviour of electrons.

Answer 1

Hint: According to the question one must know about the concept of de Broglie wavelength associated with the particle. And then only one can solve this question. When studying quantum mechanics, the de Broglie wavelength is a key idea. De Broglie wavelength is the wavelength () that is connected to an item concerning its momentum and mass. Typically, a particle's force is inversely proportional to its de Broglie wavelength.

Formula used: ${\lambda _{dB}} = \dfrac{h}{p}$
Where h is a Planck’s constant.
p is momentum and
${\lambda _{dB}}$ is de Broglie’s wavelength

Complete Step by Step Solution:
As we know that the de Broglie wavelength concept is associated with the particle i.e., ${\lambda _{dB}} = \dfrac{h}{p}$,

From here we can see that de Broglie’s wavelength is inversely proportional to the momentum and directly proportional to Planck’s constant. This means as the momentum will increase the value of de Broglie wavelength will decrease.
Therefore the correct answer is option (c).

Note: Note that the S.I unit of de Broglie wavelength is meter (m). By analysing the diffraction pattern created as electrons flow through a crystalline substance, we can deduce that matter has a wave-like character. The pattern appears when the electrons' de Broglie wavelength and the distance between their atoms in the crystals are similar.