Physics Help Forum mass of photon

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 Dec 23rd 2009, 09:45 AM #1 Banned   Join Date: Jul 2009 Posts: 66 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.
 Dec 24th 2009, 12:39 AM #2 Physics Team   Join Date: Feb 2009 Posts: 1,425 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
Dec 24th 2009, 03:12 AM   #3
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 Originally Posted by physicsquest 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?

 Dec 24th 2009, 03:23 AM #4 Physics Team     Join Date: Jul 2009 Posts: 310 r.samanta, I believe it must be the relativistic mass because a photon does not have mass non-relativistically (rest mass). __________________ "Dissent is the highest form of patriotism." - Thomas Jefferson. "Give me control of a nation's money and I care not who makes her laws." -Mayer Amschel Rothschild I study Mathematical Physics at the University of Waterloo. -DC Last edited by Deco; Dec 24th 2009 at 03:33 AM.
 Dec 24th 2009, 03:26 AM #5 Senior Member   Join Date: Sep 2009 Location: india Posts: 409 thanks for the confirmation.
Dec 26th 2009, 11:34 AM   #6
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 Originally Posted by binayakafle 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.

 Dec 26th 2009, 09:35 PM #7 Physics Team   Join Date: Feb 2009 Posts: 1,425 Hey thanks. Didnt realise that could be done!
Dec 27th 2009, 04:19 AM   #8
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 Originally Posted by physicsquest 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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# definition of dynamic mass of a photon

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