Finding the mass of a photon with given wavelength

AI Thread Summary
To find the mass of two photons with a wavelength of 4.22x10^-7 m, the energy of one photon is calculated using E=hf, resulting in E=4.71x10^-19 J. The initial calculation mistakenly used the energy for one photon to find mass, yielding M=5.23x10^-36 kg. The correct approach involves recognizing that the total energy for two photons should be used, leading to M=2E/c^2, which gives the correct mass of 1.047x10^-35 kg. It's important to include units in calculations and understand that energy is a property, not a substance.
Physics53
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Hi, stuck on this question, hoping someone could help
1. Homework Statement

Two identical photons of wavelength 4.22x16^-7m are created when a certain amount of matter M, is converted into energy, calculate the Mass (M)

The Attempt at a Solution


E= hf which is hc/wavelength
E= 4.71x10^-19J
E= mc^2
so M= E/c^2
M= 4.71x10^-19J/ 3.00x10^8^2
M= 5.23x10^-36 kg
BUT the answer is 1.047x10^-35 kg, how?[/B]
 
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First of all. Never leave out the units as here:
Physics53 said:
of wavelength 4.22x16^-7 are
The relevant unit here is meters. Without the unit, the value has no meaning.

Second
Physics53 said:
is converted into energy
Light is not converted into energy. Energy is not a substance, it is a property and it was the same before the mass was converted into the photons.

Physics53 said:
M= 4.71x10^-19J/ 3.00x10^8
You are missing the square here (and the units of c!) and the fact that you are only computing the mass corresponding to the energy of one photon, not two.

Physics53 said:
M= 5.23x10^-35 kg
The 5.23 is correct with one photon, but you made an error with the exponent, which should be 10^-36.
 
Orodruin said:
First of all. Never leave out the units as here:

The relevant unit here is meters. Without the unit, the value has no meaning.

Second

Light is not converted into energy. Energy is not a substance, it is a property and it was the same before the mass was converted into the photons.You are missing the square here (and the units of c!) and the fact that you are only computing the mass corresponding to the energy of one photon, not two.The 5.23 is correct with one photon, but you made an error with the exponent, which should be 10^-36.
Sorry about that, those were typos, fixed them up now, also i understood the notion that we were finding the mass of one photon, but how would i mathematically solve it
thanks
 
If I do M=2E/c^2 is get the correct answer which is 1.047x10^-35, but where did the 2 come from ( i just did trial and error method right now).
 
Physics53 said:
3. The Attempt at a Solution
E= hf which is hc/wavelength
E= 4.71x10^-19J
E= mc^2
so M= E/c^2
M= 4.71x10^-19J/ 3.00x10^8^2
M= 5.23x10^-36 kg
BUT the answer is 1.047x10^-35 kg, how?

the energy you have calculated is just for one photon , so to get the full energy just multplay E by 2 then convert it to mass .
 
patric44 said:
the energy you have calculated is just for one photon , so to get the full energy just multplay E by 2 then convert it to mass .
Thanks
 
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