Question

In: Physics

Microwaves have wavelengths ranging from about one meter to one millimeter. What are the ranges of...

  1. Microwaves have wavelengths ranging from about one meter to one millimeter. What are the ranges of energies and frequencies of microwaves?

Solutions

Expert Solution

We know that microwaves are electromagnetic radiations. Hence, it is quite obvious that they would travel with the speed of light.

Now, wavelength of microwaves have range 1mm to 1m

Let us first calculate the frequency correspond to lower value of wavelength i.e 1 mm

It must be noted that wavelength k and frequency v are related as

c = vk. ..... Eqn 1

Where c is the velocity of light=3*108 m/s

Putting k =1mm = 10-3 m and value of c in eqn 1 we get

3*108= v*10-3

Or v =3*108/10-3

=3*108*103

v = 3*1011 Hz .... Lower limit of frequency

Corresponding to this, we can calculate energy of microwaves by the formula

E = hv... Eqn 2

Where h is the Planck's constant=6.626*10-34 Js

Hence, Energy E = 6.626*10-34*3*1011

= 19.878*10-23 J

Now, for upper limit of wavelength k = 1 m

We again use the eqn 1

3*108= v*1

v =3*108 Hz

Further, energy corresponding to upper limit of frequency, v =3*108  m/s is given by again using eqn 2

E = 6.626*10-34*3*108

= 19.878*10-26 J


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