The maximum electron density in the ionosphere in the morning is 10...

Given, the maximum electron density in the morning

{N}_\max = {10}^{10}m^{- 3}

{f}_c^{'} = 9{\left({N}_\max\right)}^{1 / 2} = 9{\left({10}^{10}\right)}^{1 / 2}

Critical frequency ${f}_c^{′} = 9 \times {10}^{5}$

The maximum electron density at noon

{N}_\max = {2 \times 10}^{10}m^{- 3}

Critical frequency

{f}_c^{′′} = 9 \times \left({N}_\max^{′}\right)\dfrac{1}{2} = 9 \times \left(2 \times {10}^{10}\right)\dfrac{1}{2} = 9 \times \sqrt{2} \times {10}^{5}

The ratio of critical frequency at noon and critical frequency in the morning.

$\dfrac{{f}_c^{′′}}{{f}_c^{′}} = \dfrac{9 \times \sqrt{2} \times {10}^{5}}{9 \times {10}^{5}}$

Or $\dfrac{{f}_c^{′′}}{{f}_c^{′}} = \sqrt{2} = 1.414$