For sky wave propagation, the radio waves must have a frequency range in between:

Sky wave propagation involves radio waves being reflected back to Earth by the ionosphere. For this reflection to occur effectively, the frequency of the radio waves must lie within a specific range. If the frequency is too low, the waves get absorbed by the ionosphere, especially in the D layer during the day. If the frequency is too high, the waves penetrate the ionosphere and do not return to Earth.

The critical frequency, denoted as $$f_c$$, is the maximum frequency at which a radio wave can be reflected back to Earth when sent vertically upwards. It is calculated using the formula:

where $$N_{\text{max}}$$ is the maximum electron density in the ionosphere. A typical value for $$N_{\text{max}}$$ is $$10^{12}$$ electrons per cubic meter. Substituting this value:

Since $$\sqrt{10^{12}} = (10^{12})^{1/2} = 10^{6}$$ (because $$12 \times \frac{1}{2} = 6$$), we get:

Converting Hz to MHz (where $$10^6$$ Hz = 1 MHz), this becomes:

However, for oblique incidence (waves sent at an angle), the maximum usable frequency (MUF) is higher than $$f_c$$ and is given by:

where $$\theta$$ is the angle of incidence. For long-distance communication, $$\theta$$ is large, so $$\cos \theta$$ is small, allowing MUF to be significantly higher than $$f_c$$. Typically, the MUF can reach up to about 25-30 MHz under favorable conditions.

The effective frequency range for sky wave propagation is generally from 3 MHz to 30 MHz. Frequencies below 3 MHz are prone to absorption, while frequencies above 30 MHz tend to penetrate the ionosphere. Now, examining the options:

• Option A: 1 MHz to 2 MHz - This is too low; absorption occurs in the D layer.
• Option B: 5 MHz to 25 MHz - This falls within the typical 3 MHz to 30 MHz range.
• Option C: 35 MHz to 40 MHz - This is too high; waves penetrate the ionosphere.
• Option D: 45 MHz to 50 MHz - This is also too high; penetration occurs.

Therefore, the correct frequency range for sky wave propagation is given in Option B.

Hence, the correct answer is Option B.