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(A) The critical frequency $(f_c)$ of the ionosphere is given by the formula: $f_c \approx 9 	imes (N_{max})^{1/2}$, where $N_{max}$ is the maximum e

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$2$

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(A) The critical frequency $(f_c)$ of the ionosphere is given by the formula: $f_c \approx 9 	imes (N_{max})^{1/2}$, where $N_{max}$ is the maximum electron density in $	ext{electrons/m}^3$.Given $N_{max} = 10^{11} 	ext{ m}^{-3}$.Substituting the value: $f_c \approx 9 	imes (10^{11})^{1/2} = 9 	imes \sqrt{10} 	imes 10^5 \approx 9 	imes 3.16 	imes 10^5 \approx 28.44 	imes 10^5 	ext{ Hz} \approx 2.84 	ext{ MHz}$.Since the wave is reflected back if its frequency is  <  or equal to the critical frequency, among the given options, $2 	ext{ MHz}$ is the only frequency that will be reflected back by the ionosphere.

In short wave communication, waves of which of the following frequencies will be reflected back by the ionospheric layer having an electron density of $10^{11} \text{ per } m^3$ (in $\text{ MHz}$)?

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