Ionospheric Propagation: For an F1 layer with maximum electron density Nmax = 2.3 × 10^4 electrons/cm^3, compute the critical frequency.

Difficulty: Medium

Correct Answer: 1360 MHz

Explanation:


Introduction / Context:
Critical frequency is the highest frequency that will be reflected back to Earth by an ionospheric layer at normal incidence. It depends on peak electron density in that layer, a key parameter in HF radio communications.


Given Data / Assumptions:

  • Nmax = 2.3 × 10^4 electrons/cm^3 (F1 layer).
  • Use standard empirical relation for critical frequency at normal incidence.


Concept / Approach:
A common engineering rule is fo(MHz) ≈ 9 × √(Nmax), when Nmax is expressed in electrons/cm^3 (for a quick estimate). We directly substitute Nmax and compute fo.


Step-by-Step Solution:

Step 1: Compute √(Nmax) = √(2.3 × 10^4) ≈ √23000 ≈ 151.66.Step 2: Multiply by 9: fo ≈ 9 × 151.66 ≈ 1364.9 MHz.Step 3: Round to given options: 1360 MHz is the closest choice.


Verification / Alternative check:

Back-calculate: (1360/9)^2 ≈ (151.1)^2 ≈ 2.28 × 10^4 electrons/cm^3, matching Nmax within rounding.


Why Other Options Are Wrong:

1.36, 13.6, 136 MHz: Too low by factors of 10^3, 10^2, and 10, respectively.0.136 MHz: Grossly inconsistent with the computed root.


Common Pitfalls:

Applying the formula with inconsistent units (m^-3 vs cm^-3); forgetting to express the result in MHz.


Final Answer:

1360 MHz

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