Question

The ionosphere, which is the layer of atmosphere located in the region 50-5000 km above the Earth, has a density of free electrons just like a metal.

a. if the free electron density is 10^6 electrons per cubic centimeter, determine the plasma frequency of the ionosphere in hertz (Hz)

b. a metal is transparent to radiation with frequencies higher than the free electron plasma frequency (this is usually in the ultraviolet range), and reflect at lower frequencies. Determine the wavelengths at which the ionosphere becomes transparent, and those which it is reflecting.

c. It is transparent to at least some radio waves? (This is important consideration for communication with satellites and spacecraft

Answer 1

given

the layer of atmosphere located in the region 50-5000 km above the Earth

a )

the free electron density is 10⁶ electrons per cubic centimeter

n_e = 10⁶ electrons/cm³

n_e = 10¹² electrons/m³

the frequency formula f = ( n_e e² / m _o )^1/2

here e = 1.6 x 10^-19 C

m = 9.11 x 10^-31 kg

_o = 8.85 x 10^-12 F/m

= ( 10¹² x 1.6 x 10^-19 / 9.11 x 10^-31 x 8.85 x 10^-12 )^1/2

f = 56349382.19 Hz

the plasma frequency of the ionosphere in hertz is f = 56.34 x 10⁶ Hz

b )

here

a metal is transparent to radiation with frequencies higher than the free electron plasma frequency

(this is usually in the ultraviolet range),

and

reflect at lower frequencies

so the wavelength equation = C / f

= 3 x 10⁸ / 56349382.19

= 5.324 m

so mentioned above wavelength is an ionosphere is highly reflecting less of this wavelength and above of

transparent.

c )

"YES"

It is transparent to at least some radio waves.