Derive relation between wavelength and momentum
Answers
Explanation:
λ= p/h
where, λ=wavelength
h=Planck′ s constant
p=momentum
Answer:
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
λ=vf
Where
λ= 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,
λα1M
Replacing the proportionality sign with equal to we will get a proportionality constant which is ,
λ=kM
Here,
k = h = Planck’s Constant
Now we can write the above equation as,
λ=hM
Where,
λ= Wavelength
h = Planck’s Constant
M= Momentum
There the relation between wavelength and momentum of a moving particle is
λ=hM
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.
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