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Will two photons with equal wavelength have same linear momentum?

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closed as off-topic by Yashas, honeste_vivere, Kyle Kanos, ZeroTheHero, Jon Custer Jul 27 '17 at 11:41

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    $\begingroup$ If you look up the definition of relativistic momentum for a photon, you will be able to answer your own question. What I will add is that momentum is a vector and direction matters... $\endgroup$ – Paul Jul 26 '17 at 12:47
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Usually, it is known that the energy and momentum of a photon depend only in its frequency (or inversely, its wavelength). The frequency of a photon is denoted by $\nu$ and it is measured in $Hertz$ while the wavelength is denoted by $\lambda$ and it has the SI unit of length.

$E=h\nu=\frac{hc}{\lambda}$ is the energy. Now, for the momentum, you have the following formula $$\textbf{p}=\hbar\textbf{k}$$, with $\textbf{k}$ being the wave vector. The magnitude of the wave-vector is $k=|k|=2\pi/\lambda$. the vector $\textbf{p}$ points in the direction of the propagation of the photon, so the magnitude of the momentum is $$p=\frac{h}{\lambda}$$ known as the de Broglie's formula.

So, to answer your question, if the two photons have the same frequency, they have the same magnitude for the momentum $p_1=p_2=\frac{h\nu}{c}$.

Of course, there is more beyond this theory. I recommend you to read about wave-vector and photons. w-v ; photon

I hope this helps :)

LE: As garyp said, this is valid only in vacuum.

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  • $\begingroup$ Note that this answer is restricted to radiation in the vacuum. $\endgroup$ – garyp Jul 26 '17 at 14:10
  • $\begingroup$ Yeah. You're right! $\endgroup$ – Robert Poenaru Jul 26 '17 at 16:08

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