Question

Which is the de – Broglie equation?
A. \[h = p\lambda \]
B. \[h = p{\lambda ^{ - 1}}\]
C. \[h = {p^{ - 1}}\lambda \]
D. \[h = p + \lambda \]

Answer 1

Hint: The de – Broglie equation of a wave gives us the relationship between the momentum of the wave and its wavelength. All matter exhibits wave-like behaviour.

Complete step by step answer:
The de – Broglie equation states that a matter can act as a wave like the light can behave as waves and particles. All matter exhibits wave-like behaviour. For example, a beam of electrons can be diffracted just like a beam of light or a water wave.
This concept that matter behaves like a wave was proposed by Louis de Broglie in 1924. It is also known as the de Broglie hypothesis. Matter waves are referred to as de Broglie waves. Therefore, if we look at every moving particle whether it is microscopic or macroscopic it will have a wavelength. The objects big enough to observe (macroscopic objects) will have a wave nature that is visible.
The de – Broglie equation basically describes the wave nature of the electron. Broglie in his thesis suggested that any moving particle, whether microscopic or macroscopic, will be associated with a wave character called ‘Matter Waves’. He further proposed a relation between the velocity and momentum of a particle with the wavelength if the particle had to behave as a wave. He stated that the wavelength of the matter wave is inversely proportional to its momentum. The constant of proportionality is called Planck's constant, denoted by ‘h’. Mathematically:
\[\lambda = \dfrac{h}{p}\]
Or \[\lambda p = h\]

Hence, the correct answer is (A).

Note: Remember that this equation is valid only for the wave nature of a particle. This equation can’t be used for finding the wavelength of photons incident on a metal surface.