Question

What is the relation between wavelength and momentum of moving particles?

Answer 1

Hint: When a particle moves it has its own wavelength and momentum created around it. When a particle's wavelength increases its momentum decreases as it has an inverse relation. Using this statement we can write the solution.

Complete step by step solution:
Wavelength is generally defined as the distance between two successive crests or troughs of a wave. It is measured in the direction of the wave due to which it generates an inverse relationship between wavelength and frequency.
Formula for wavelength is thus represented as
$\lambda = \dfrac{v}{f}$
Where
$\lambda = $ Wavelength
$v = $ Velocity
$f = $ Frequency
Here the wavelength is also known as De Broglie wavelength .
Momentum:
It is defined as the property of a moving body which is measured by the help of its mass and velocity with which the body is moving.
As we all know that a body having some mass and some motion in it is called momentum.
Formula for momentum is thus represented as
$M = mv$
Where
$m = $ Mass of the body
$v = $ Velocity
Now,
Relation between wavelength and momentum is as follows
As we know ,
Wavelength and momentum are inversely proportional to each other
Then,
$\lambda \,\alpha \,\dfrac{1}{M}$
Replacing the proportionality sign with equal to we will get a proportionality constant which is ,
$\lambda = \dfrac{k}{M}$
Here,
${\text{k = h = }}$ Planck’s Constant
Now we can write the above equation as,
$\lambda = \dfrac{h}{M}$
Where,
$\lambda = $ Wavelength
${\text{h = }}$ Planck’s Constant
$M = $ Momentum
There the relation between wavelength and momentum of a moving particle is
$\boxed{\lambda = \dfrac{h}{M}}$

Note:
Here the constant value can be calculated by using the dimensional formula of wavelength and momentum of a moving particle. Remember this relation will help you to solve the problem related to wavelength and momentum.