Question

The momentum of a particle having a de- Broglie wavelength of ${10^{ - 17}}{\text{m}}$ is:
(Given: ${\text{h}} = 6.625 \times {10^{ - 34}}{\text{m}}$)
A. $3.3125 \times {10^{ - 7}}{\text{kg m }}{{\text{S}}^{ - 1}}$
B. $26.5 \times {10^{ - 7}}{\text{kg m }}{{\text{S}}^{ - 1}}$
C. $6.625 \times {10^{ - 17}}{\text{kg m }}{{\text{S}}^{ - 1}}$
D. $13.25 \times {10^{ - 17}}{\text{kg m }}{{\text{S}}^{ - 1}}$

Answer 1

Hint: To answer this question, you must recall the formula for de Broglie’s wavelength of an electron. De Broglie proposed a theory suggesting that every form of matter behaves like waves in some or the other circumstances.
Formula used:
 $\lambda = \dfrac{h}{{mv}} = \dfrac{h}{p}$
Where, $\lambda $ is the de- Broglie wavelength of the matter wave
$h$ is Planck’s constant
$m$ is the mass of the given particle under consideration
$v$ is the velocity of the given particle under consideration
And $p$ is the momentum of the particle

Complete step by step answer:
We are supposed to find the momentum of a particle whose wavelength is provided to us. We can use the de- Broglie equation directly to get the momentum of the particle.
It is given to us in the question that the value of Planck’s constant is given as ${\text{h}} = 6.625 \times {10^{ - 34}}{\text{m}}$.
We know from the de- Broglie equation that $\lambda = \dfrac{h}{{mv}} = \dfrac{h}{p}$.
Or we can write, $p = \dfrac{h}{\lambda }$.
Substituting the values, we get,
$p = \dfrac{{6.625 \times {{10}^{ - 34}}}}{{{{10}^{ - 17}}}}$
$\therefore p = 6.625 \times {10^{ - 17}}{\text{ kg m }}{{\text{s}}^{ - 1}}$

Thus, the correct answer is C.

Note:
Matter waves are a crucial part of the quantum mechanical theory, being an example of the dual nature of matter. It was suggested that all matter particles exhibit a wave-like behaviour which may or may not be significant enough. For instance, a beam of electrons is diffracted in the same way like a beam of light or a water wave does. In most cases, the wavelength of objects is too small to have a significant impact on our day-to-day activities. Hence in our day-to-day lives, with objects of the size of tennis balls or with people, matter waves are not of significant wavelength. These matter waves are referred to as de Broglie waves.