How Does Changing Wavelength Affect the Power of a Light Source?

[googlyeyes]

Homework Statement

The WSFM radio station (which broadcasts at 101.7MHz) emits 1.78x10^29 photons per second and has an effective radiated power of 12kW.

If the same number of photons were emitted as visible light, what would be the power of the light source?

Homework Equations

P=W/t

The Attempt at a Solution

P = (1.78x10^29)x[(6.626x10^-34)x(3x10^8)/λ]

 

[BOYLANATOR]

Homework Statement

P = (1.78x10^29)x[(6.626x10^-34)x(3x10^8)/λ]

Strictly speaking, for dimensions the right hand side should be "per second".

Is the problem that you don't know the wavelength?

 

[googlyeyes]

There are actually multiple parts to this question. Would you like me to type them up with my working for those as well (as that may also be wrong)

 

[BOYLANATOR]

Well you can do if you need help with them, however, there is enough information here already for you to answer this question.

 

[googlyeyes]

I will post it anyway:

QUESTION: Radio station WSFM broadcasts at 101.7MHz with an effective radiated power of 12kW.
(a) What is the value of the momentum of each radiated photon
(b) If an electron had the same momentum, how fast would the electron be travelling?
(c) How many photons does WSFM emit every second?
(d) If the same number of photons were emitted as visible light, what would be the power of this light source?

ANSWERS (so far):
(a) p=2.246x10^-34
(b) p=mv thus v=(2.246x10^-34)/(9.10938x10^-31) thus v=0.000247m/s
(c) 1.78x10^29
(d) P = (1.78x10^29)x[(6.626x10^-34)x(3x10^8)/λ]

 

[BOYLANATOR]

Ok, I'm not going to check the numbers but they look in the right ballpark. For (d) you are going to have to pick a suitable wavelength for visible light. This is common in these types of questions. Perhaps that helps?

 

[googlyeyes]

Ok well I am pretty sure that visible light has a wavelength between around 400-700nm but doesn't that mean there are so many wavelengths that could be chosen and thus many different answers to the question?

 

[BOYLANATOR]

Yeah. You could work out the minimum and maximum and give the full range of answers, usually I just pick 500nm and run with that.