The maximum electron density in the ionospherein the mornong is `10^(10)m^(-3)`. At noon time it increases to `2xx10^(10)m^(-3)`. Find the ratio of critical frequency at noon and the critical frequency in the morning.

Options

A. `2.00`
B. `2.82`
C. `4.00`
D. `1.414`

Answer

D

Explanation

Given the maximum electron density in the morning,
`N_("max")=10^(10)m^(-3)`
`:.` Critical frequency
`f_(c)^(')=g(N_("max"))^(1//2)`
`=9(10^(10))^(1//2)=9xx10^(5)`
The maximum electron density at noon
`N_("max")=2xx10^(10)m^(-3)`
`:.` Critical frequency
`f_(c)^('')=9xx(N_("max")^('))^(1//2)`
`=9xx(2xx10^(10))^(1//2)=9xxsqrt(2)xx10^(5)`
The ratio of critical frequencies at noon and in the morning is
`(f_(c)^(''))/(f_(c)^('))=(9xxsqrt(2)xx10^(5))/(9xx10^(5))`
or `(f_(c)^(''))/(f_(c)^('))=sqrt(2)=1.414`