Which of the following equation correctly represents the momentum of a photon of energy E

Question Id: PH0000003

Question: Which of the following equation correctly represents the momentum of a photon of energy E?

(a) \(\frac{E}{c}\)

(b) \(E^{2}c\)

 (c) \(Ec\)

 (d) \(Ec^{2}\)

Solution:

Here, option (a) \(\frac{E}{c}\) is the correct answer.

Explanation:

Energy carried by a photon having frequency \(\nu\) is \(E=h\nu\) ; Where \(h\) is Plank's constant.

\(\Rightarrow E=\frac{hc}{\lambda}\)

\(\Rightarrow \lambda=\frac{hc}{E}\) ; Where \(\lambda\) is wavelength and \(c\) is velocity of light.

We know the de Broglie wavelength \(\lambda=\frac{h}{p}\) 

\[\Rightarrow p=\frac{h}{\lambda}\]

\(\Rightarrow p=\frac{h}{\frac{hc}{E}}\) ; putting the value of \(\lambda\)

\[\Rightarrow p=\frac{hE}{hc}\]

\[\Rightarrow p=\frac{E}{c}\]

So, this is the equation of momentum of a photon.

 

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