Hello Friends I am Asad . In this article I am going to explain if p=mv then why massless photons have momentum .
So let's start this
To understand this topic you must need basic knowledge of Mass
What is mass and it's classification
The amount of matter in any body is called Mass . Mass is the measurement of Inertia .
There are two types of mass
1 . Rest Mass
2 . Relative Mass
The mass we know is called rest mass . But when a body is moving with high speed , the mass of that body get increased . It sounds weird but it's true . According to the Einstein's theory of relativity If an object moves with high velocity the mass of that object is greater than that object's mass in rest motion .
If an object's rest mass is m. (m not) and moving with v velocity then the relative mass of that object is
m = m. / (1-(v²÷c²))
where c = speed of light .
What are photons ?
We know that light has dual nature
1 . wave
2 . Particles
When light behave like particles , it contains a kind of particles which are called photons .
Now let's go to the main point . We all have read in high school that p=mv where ,
P = momentum
m = rest mass
V = velocity of the object
If p=mv then how could photons have momentum when they have no mass ?
p = mv , with this equation we can easily calculate the momentum of any heavy that is moving with low speed . But in the case of a object which has zero mass and moving with the near speed of light we can't calculate the momentum with that equation . To calculate the momentum of any object like photons , we don't need Mass . We can calculate the momentum without mass .
The equation we know E = mc² is not the complete equation . The complete equation is
E² = p²c² + m²c⁴ where
E = Energy
p = momentum
m = rest mass
c = speed of light
I'm not going to derived this equation but you can see the derivation from this Link .
In this equation if we put the rest mass of photons which is zero we will get this
E² = p²c²
We can write this like
=> E = pc
=> p = E /c
So with this equation we can see that we don't need Mass to calculate the momentum of photons . We just need the amount of energy .
I hope you understood it . If you have any questions comment below .
Thanks for reading .
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