Determine the rate of emission of quanta from the station

[queenstudy]

Homework Statement

A radio station operates at a frequency 103.7MHz with a power output of 200kW.
1)Determine the rate of emission of quanta from the station.
2)If we treat the radio station as a point source radiatng uniformly in all directions, find the number of photons inside a cubical radio 20cm on a side located 15km away from the radio station

Homework Equations

The Attempt at a Solution

1) i solved it by finding the energy of one photon and then N/t= 200000/Energy of one photon =2.91 *10^30 quanta/s
2) I thought that the power i have should be multiplied by 4∏d^2 / a^2 where a is the side of the radio and d is the distance from the source to the radio box and then i have the time needed to reach the dario which is d/c so the number of photons is to be 2.75*10^10 photons but it didnt please help

 

[mathfeel]

Homework Statement

A radio station operates at a frequency 103.7MHz with a power output of 200kW.
1)Determine the rate of emission of quanta from the station.

1) i solved it by finding the energy of one photon and then N/t= 200000/Energy of one photon =2.91 *10^30 quanta/s

Didn't check your math, but the argument is correct.

2)If we treat the radio station as a point source radiatng uniformly in all directions, find the number of photons inside a cubical radio 20cm on a side located 15km away from the radio station

2) I thought that the power i have should be multiplied by 4∏d^2 / a^2 where a is the side of the radio and d is the distance from the source to the radio box and then i have the time needed to reach the dario which is d/c so the number of photons is to be 2.75*10^10 photons but it didnt please help

Not sure how did you get the "size of the radio". But dividing the power by the area of the sphere of radius d, you get power per area (Intensity):
[itex]I = P/A[/itex]
Intensity is related to energy density [itex]u[/itex] (energy per volume) and speed [itex]v[/itex] of photon by:
[itex]I = u v[/itex]
From energy density, you can calculate photon density. Then using the volume of the radio, you can compute the number of photons. I got 2.74e10 photons.

 

[queenstudy]

that is the exact answer thank you mathfeel

 

[queenstudy]

Didn't check your math, but the argument is correct.


Not sure how did you get the "size of the radio". But dividing the power by the area of the sphere of radius d, you get power per area (Intensity):
[itex]I = P/A[/itex]
Intensity is related to energy density [itex]u[/itex] (energy per volume) and speed [itex]v[/itex] of photon by:
[itex]I = u v[/itex]
From energy density, you can calculate photon density. Then using the volume of the radio, you can compute the number of photons. I got 2.74e10 photons.

can you tell me how did you calculate the energy density and photon density?

 

[mathfeel]

can you tell me how did you calculate the energy density and photon density?

In my reply #2, I gave two definitions of the same quantity I. By equating them, you can compute u.

u is energy / volume. You also know how much energy is in each photon. So you can get photon / volume.

 

[queenstudy]

thank you very much i now understand it , the good thing is learning a new concept called photon density