Q144 / 180 · AIIMS 2005 · Physics

For skywave propagation of a $10 \mathrm{MHz}$ signal, what should be the minimum electron density in ionosphere?

  • Correct answer
    A
    $\sim 1.2 \times 10^{12} \mathrm{~m}^{-3}$
  • B
    $\sim 10^6 \mathrm{~m}^{-3}$
  • C
    $\sim 10^{14} \mathrm{~m}^{-3}$
  • D
    $\sim 10^{22} \mathrm{~m}^{-3}$.

Solution

The critical frequency of a sky wave for reflection from a layer of atmosphere is given by $$ f_c=9\left(N_{\max }\right)^{1 / 2} $$ where $N$ is the density of electron $/ \mathrm{m}^3$. $$ \begin{aligned} 10 \times 10^6 & =9\left(N_{\max }\right)^{1 / 2} \\ N_{\max } & =\left(\frac{10 \times 10^6}{9}\right)^2 \simeq 1.2 \times 10^{12} \mathrm{~m}^{-3} \end{aligned} $$

Hence, the correct answer is option: 'A'.

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