$\lambda=\frac{h}{p}$

hkular_2L
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How can a photon have no rest mass, but still have momentum?

904564128
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Momentum is also equal to the product of energy and velocity. Since a photon has energy and velocity, it can therefore have momentum, even though it does not have a mass.

Chem_Mod
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Firstly, momentum, as it is usually defined, is p = mv. However, this is not what is called a scalar quantity, it is a vector and has direction and therefore not very generalizable. The more general unit of measure is energy. For example, I can have a particle not moving and under no gravity but it still has energy, E = mc2. If I tried to write down its momentum, it would be 0 and, mathematically, it does not exist if we just considered its momentum.

Writing momentum in terms of energy, $E = \frac{1}{2}mv^{2} = \frac{p^{2}}{2m}$. Now of course, we still have to contend with the m on the denominator. However going towards representing systems in terms of their energy is a good first step.

What comes next is from physics and general relativity. The total energy of a relativistic particle, things near the speed of light, is:
$E^{2} = p^{2}c^{2} + m^{2}c^{4}$
setting m = 0:

$E = pc$

$p = \frac{E}{c}$

The first part has nothing to do with the answer, it is just an introduction towards writing things in terms of its energy, scalars, instead of vectors.

Even though momentum is a vector and energy is scalar, photons do have momentum when they hit a surface. Note when a photon hits a surface it ceases to exist and its energy has been transferred to the surface.

Unlike a bullet after it hits a surface it still has mass (exists)