On a particular day, the maximum frequency reflected from the ionosphere is 10 MHz The maximum electron density in ionosphere is

Options

A. `10^(6)//m^(2)`
B. `10^(12)//m^(3)`
C. `1.23 xx 10^(12)//m^(3)`
D. `1//9 xx 10^(6)//m^(3)`

Answer

To find the maximum electron density in the ionosphere given the maximum frequency reflected, we can use the formula:

\[ n_{max} = \frac{f_{max}^2}{81} \]

Where:
- \( n_{max} \) is the maximum electron density (in electrons per cubic meter).
- \( f_{max} \) is the maximum frequency reflected (in Hz).

### Step-by-Step Solution:

1. **Identify the given frequency**:
The maximum frequency reflected from the ionosphere is given as \( f_{max} = 10 \, \text{MHz} \).
- Convert this frequency into Hertz (Hz):
\[ f_{max} = 10 \, \text{MHz} = 10 \times 10^6 \, \text{Hz} = 10^7 \, \text{Hz} \]

2. **Substitute the frequency into the formula**:
Now, substitute \( f_{max} \) into the formula for maximum electron density:
\[ n_{max} = \frac{(10^7)^2}{81} \]

3. **Calculate \( (10^7)^2 \)**:
\[ (10^7)^2 = 10^{14} \]

4. **Divide by 81**:
Now, we can calculate \( n_{max} \):
\[ n_{max} = \frac{10^{14}}{81} \]

5. **Perform the division**:
To find \( n_{max} \), we can perform the division:
\[ n_{max} \approx 1.2345679 \times 10^{12} \, \text{m}^{-3} \]
For simplicity, we can round this to:
\[ n_{max} \approx 1.23 \times 10^{12} \, \text{m}^{-3} \]

6. **Final result**:
Thus, the maximum electron density in the ionosphere is:
\[ n_{max} \approx 1.23 \times 10^{12} \, \text{electrons/m}^3 \]

### Conclusion:
The maximum electron density in the ionosphere on that particular day is approximately \( 1.23 \times 10^{12} \, \text{m}^{-3} \).

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