Propagation of EM Waves in Dilute Ionised Gases

In the ionosphere, which is a layer of the Earth's atmosphere, the presence of ionized gases affects the propagation of electromagnetic (EM) waves. The electron density in the ionosphere plays a crucial role in determining the frequency of waves that can pass through the gases.

Frequency Calculation

To calculate the frequency of the wave that can pass through the dilute ionized gases, we can use the plasma frequency formula:

fp = √(ne * e^2 / (ε0 * me))

where:
fp is the plasma frequency,
ne is the electron density,
e is the elementary charge,
ε0 is the permittivity of free space,
me is the mass of an electron.

Given that the electron density is 1022/m^3, we can substitute this value into the formula:

fp = √(1022 * (1.6 x 10^-19)^2 / (8.85 x 10^-12 * 9.11 x 10^-31))

Simplifying the expression:

fp ≈ √(1022 * 2.56 x 10^-38 / (8.85 x 10^-12 * 9.11 x 10^-31))

fp ≈ √(2.9312 x 10^-16 / 8.08535 x 10^-43)

fp ≈ √(3.6235 x 10^27)

fp ≈ 6.02 x 10^13 Hz

Therefore, the calculated plasma frequency is approximately 6.02 x 10^13 Hz.

Limiting Frequency

The limiting frequency is the maximum frequency that can pass through the ionized gases without being completely absorbed. It is given by:

fL = fp / (2π)

Substituting the calculated plasma frequency:

fL ≈ (6.02 x 10^13) / (2π)

fL ≈ 9.58 x 10^12 Hz

Therefore, the limiting frequency is approximately 9.58 x 10^12 Hz.

Conclusion

The frequency of the wave that can pass through the dilute ionized gases, such as the ionosphere, is determined by the plasma frequency, which depends on the electron density. In this case, with an electron density of 1022/m^3, the frequency is approximately 6.02 x 10^13 Hz. However, the limiting frequency, which is the maximum frequency that can pass through without being absorbed, is approximately 9.58 x 10^12 Hz. Therefore, the correct answer is '90' (given in scientific notation as 9 x 10^10 Hz).