In short wave communication, waves of which of the following frequencies will be reflected back by the ionoshperic layer having electron density `10^11 " per " m^3`

Options

A. 2 MHz
B. 10 MHz
C. 12 MHz
D. 18 MHz

Explanation

To solve the problem, we need to determine the critical frequency of the ionosphere based on the given electron density and then identify which frequencies will be reflected back by the ionosphere.

### Step-by-Step Solution:

1. **Understanding the Critical Frequency Formula**:
The critical frequency (U_c) of the ionosphere can be calculated using the formula:
\[ U_c = 9 \sqrt{n} \]
where \( n \) is the electron density in \( \text{m}^{-3} \).

2. **Substituting the Given Electron Density**:
We are given that the electron density \( n = 10^{11} \, \text{m}^{-3} \). We can substitute this value into the formula:
\[ U_c = 9 \sqrt{10^{11}} \]

3. **Calculating the Square Root**:
The square root of \( 10^{11} \) is:
\[ \sqrt{10^{11}} = 10^{5.5} = 3.16 \times 10^{5} \]

4. **Calculating the Critical Frequency**:
Now we can calculate \( U_c \):
\[ U_c = 9 \times 3.16 \times 10^{5} = 2.84 \times 10^{6} \, \text{Hz} \]
This can be approximated to:
\[ U_c \approx 2.7 \, \text{MHz} \]

5. **Determining the Frequencies that will be Reflected**:
According to the properties of the ionosphere, frequencies less than the critical frequency will be reflected. Therefore, any frequency less than \( 2.7 \, \text{MHz} \) will be reflected.

6. **Identifying the Correct Option**:
From the options provided, we need to find which frequency is less than \( 2.7 \, \text{MHz} \). If one of the options is \( 2 \, \text{MHz} \), it is less than \( 2.7 \, \text{MHz} \) and will be reflected.

### Final Answer:
The frequency that will be reflected back by the ionospheric layer is **2 MHz**.

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