A 45 kW broadcasting antenna emits radio waves at 4 MHz, emitting 1.7x10^31 photons per second. To calculate this, the power of the antenna is converted to energy per second, then Planck's equation is used to relate the energy to a quantum of radiation at the given frequency. While electromagnetic radiation has a quantum nature, it is not important to consider here because the large number of photons emitted means the radiation can be treated classically.

1. 1
A 45 kW broadcasting
antenna emits radio
waves at a frequency of 4
MHz.
(a) How many photons
are emitted per second?
(b) Is the quantum nature
of the electromagnetic
radiation important in
analyzing the radiation
emitted from this
antenna?

2. 2
Solution
( )
We know that
1
1
45000
45000
45000
(i.e. 45000 is the
electromagnetic energy
emitted by the antenna
in one second)
a
J
W
s
J
W
s
E J
E J

 
 

According to Planck's postulate,
the energy of an oscillator of
natural frequency must be an
integral multiple of , i.e.
, 0,1,2,3,....(1)
where is a universal constant &
is the energy of
h
E nh n
h
h




 
a "quantum"
of radiation.

3. 3
34 6
28
28
28
31
31
31
Using the values of , &
in eq.(1), we get
45000J 6.626
10 . 4 10
45000 26.504
10 .
45000 26.506 10
45000 10
26.504
45 10
26.506
1.6977 10
1.7 10
E h
nX X
J sX X Hz
J nX
X J sXHz
nX X
X
n
X
n
n X
X





 
 
 
 
 


4. 4
No, the quantum nature of the
electromagnetic radiation is
not important in analyzing the
radiation emitted from this
antenna because the antenna
emits a very large number of
photons per second,
(
.
)
i.e
b
31
1.7X10 photons.
Hence, this type of radiation can
be adequately handled by classical
theory of electromagnetism.

5. 5