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:
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
Discussion & Comments