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Old Dec 23rd 2009, 09:45 AM   #1
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mass of photon

Prove that dynamic mass of photon is hv/(c^2)
where notations carry usual meaning.I know only 3 eqns
related to this but it is impossible to get proof
combining these three. Anyone please give me idea
to prove this with description.
they are: 1)E=(1/2)mv^2
2)E=mc^2
3)E=hf
This question was asked many times in past ISc
examinations and MBBS Entrance Exams of Nepal.
So,it's not a fake question. Plese help.
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Old Dec 24th 2009, 12:39 AM   #2
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The dynamic mass of the photon is hv/(c^2)

We have E = h v and E = m c^2 . Just equate the two to get

m = h v / (c^2)

Note that the second term in the numerator is nu (frequency) not v. Maybe that is what has confused you. You can confirm that it cant be v as then the dimensions wont match.

In your notation, what you have to prove is only m = h f / c^2
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Old Dec 24th 2009, 03:12 AM   #3
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Originally Posted by physicsquest View Post
The dynamic mass of the photon is hv/(c^2)

We have E = h v and E = m c^2 . Just equate the two to get

m = h v / (c^2)

Note that the second term in the numerator is nu (frequency) not v. Maybe that is what has confused you. You can confirm that it cant be v as then the dimensions wont match.

In your notation, what you have to prove is only m = h f / c^2
physicsquest, can u tell me if the 'm' you used is the relativistic mass of photon or not?
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Old Dec 24th 2009, 03:23 AM   #4
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r.samanta,

I believe it must be the relativistic mass because a photon does not have mass non-relativistically (rest mass).
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Last edited by Deco; Dec 24th 2009 at 03:33 AM.
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Old Dec 24th 2009, 03:26 AM   #5
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thanks for the confirmation.
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Old Dec 26th 2009, 11:34 AM   #6
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Originally Posted by binayakafle View Post
Prove that dynamic mass of photon is hv/(c^2)
where notations carry usual meaning.
Physicsquests derivation is correct but it requires one to know that E = mc^2. Here is a derivation which does not require the reader to know that. All the reader is required to know is the classical expression E = pc which can be derived for an EM wave.

The actual name of such a mass is inertial mass or as others like to call it, relativistic mass. The mass that people refer to when they say that the mass of a photon is zero is known as proper mass or as rest mass.

The derivation is quite simple. By definition, the inertial mas of a particle is
the m in the relation p = mv or if we're speaking only of magnitudes, p = mv. For a photon v = c and E = pc -> p = E/c. So we have E/c = mc. Solve for m to obtain m = E/c^2. The energy of a photon is related to the photon's frequency f by E = hf so we have m = hf/c^2.
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Old Dec 26th 2009, 09:35 PM   #7
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Hey thanks. Didnt realise that could be done!
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Old Dec 27th 2009, 04:19 AM   #8
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Originally Posted by physicsquest View Post
Hey thanks. Didnt realise that could be done!
You're welcome. I wouldn't know that myself unless I read a variety of relativity texts. You can't really get a broad knowledge base from one text. That's why my first physics prof's advice about reading more than one text has always come in handy. I read that derivation in both Rindler's and D'Inverno's relativity texts. It was such a beautiful derivation it made it easy to remember.
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