Finding the mass of a photon with given wavelength

[Physics53]

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]

 

[Orodruin]

First of all. Never leave out the units as here:

of wavelength 4.22x16^-7 are

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

Second

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.

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.

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.

 

[Physics53]

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

 

[Physics53]

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).

 

[patric44]

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 .

 

[Physics53]

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