AIIMS 2005 Physics Skywave Propagation MCQ Question

To determine the minimum electron density in the ionosphere necessary for skywave propagation of a 10 MHz signal, we can utilize the relationship between frequency, wavelength, and the critical electron density required for reflection of radio waves.

Key Concepts:

1. Skywave Propagation: This involves the reflection of radio waves from the ionosphere, allowing long-distance communication. The ionosphere consists of ionized particles which can reflect radio waves back to Earth.

2. Critical Frequency: The critical frequency ($f_c$) is the maximum frequency that can be reflected by the ionosphere, given by the formula:

   $f_c = 9 \sqrt{N_e}$

   where:

   • $f_c$ is the critical frequency in MHz,
   • $N_e$ is the electron density in electrons per cubic meter (m⁻³).

Step-by-Step Calculation:

Given:

• Frequency of the signal, $f = 10 \text{ MHz}$.

To find the minimum electron density ($N_e$) for skywave propagation at this frequency, we set $f_c = f$:

$10 = 9 \sqrt{N_e}$

Now, we can solve for $N_e$:

1. Rearranging the equation:

   $\sqrt{N_e} = \frac{10}{9}$

2. Squaring both sides to eliminate the square root:

   $N_e = \left(\frac{10}{9}\right)^2$

3. Calculating the square:

   $N_e = \frac{100}{81} \approx 1.2345679 \, \text{(in m}⁻³\text{)}$

4. Since we need to express this in a more manageable form, we convert it into scientific notation:

   $N_e \approx 1.2345 \times 10^{12} \, \text{m}⁻³$

From this calculation, we conclude that the minimum electron density required for a 10 MHz signal to be successfully reflected in the ionosphere is approximately $1.2 \times 10^{12} \, \text{m}⁻³$.

Explanation of Options:

• A) $1.2 \times 10^{12} \, \text{m}⁻³$: This is the correct answer, as calculated above, confirming that this density is required for reflection of a 10 MHz signal.

• B) $10^6 \, \text{m}⁻³$: This value is too low to reflect a 10 MHz signal, as it corresponds to a much lower critical frequency, approximately $3 \, \text{MHz}$.

• C) $10^{14} \, \text{m}⁻³$: This value is excessively high and would correspond to a critical frequency significantly higher than 10 MHz, indicating that while it would reflect 10 MHz, it is not the minimum required density.

• D) $10^2 \, \text{m}⁻³$: This is also far too low for 10 MHz, corresponding to a critical frequency of about $0.3 \, \text{MHz}$.

Conclusion:

Only option A provides the necessary minimum electron density for the effective skywave propagation of a 10 MHz signal, validating it as the correct choice. The calculations followed the established formulas and concepts related to ionospheric propagation.