   Chapter 29, Problem 35PE

Chapter
Section
Textbook Problem

(a) How far away must you be from a 650-kHz radio station with power 50.0 kW for there to be only one photon per second per square meter? Assume no reflections or absorption, as if you were in deep outer space. (b) Discuss the implications for detecting intelligent life in other solar systems by detecting their radio broadcasts.

To determine

(a)

The distance far away must you be from a 650 kHz radio station with power 50.00 kW for there to be only one photon per second per square meter.

Explanation

Given info:

f=650 kHz

p=50 kW

h=6.63×1034 Js

Formula used:

For energy in photon in radio waves, the relation between energy and frequency is

Ehf

Calculation:

Substituting the given values of frequency in relation with time, we get

f=1T

Substituting the values, we get

f=650×103pulses/s

Now Energy of radio waves is

E6.63×1034×650×103 JE4.31×1028 J

The number of photons per second are emitted by the flux of the satellite, we get

p=nE

Substituting the given values

n=pE

Substituting the given values of joule in term of electron volt, we get

1J=11.6×1019 eV

n=50.0×103 Js4

To determine

(b)

This implications for detecting intelligent life in other solar systems by detecting their radio broadcasts.

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