On a particular day, the maximum frequency reflected from the ionosphere is 9 MHz. On another day. It was found to increase by 1 MHz. Calculate the rate of the maximum electron densities of the ionosphere on the two days

Answer

To solve the problem of calculating the rate of maximum electron densities of the ionosphere on two different days based on the maximum frequencies reflected, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Frequencies:**
- On the first day, the maximum frequency \( f_c \) is 9 MHz.
- On the second day, the maximum frequency \( f_c' \) is 10 MHz (which is an increase of 1 MHz).

2. **Understand the Relationship Between Frequency and Electron Density:**
- The critical frequency \( f_c \) is related to the maximum electron density \( n_{max} \) by the formula:
\[ f_c = k \sqrt{n_{max}} \]
where \( k \) is a constant that depends on the units used. For our purposes, we can use \( k = 9 \times 10^6 \) Hz for simplicity.

3. **Calculate the Electron Densities:**
- For the first day (9 MHz):
\[ n_{max} = \left( \frac{f_c}{k} \right)^2 = \left( \frac{9 \times 10^6}{k} \right)^2 \]
- For the second day (10 MHz):
\[ n_{max}' = \left( \frac{f_c'}{k} \right)^2 = \left( \frac{10 \times 10^6}{k} \right)^2 \]

4. **Calculate the Ratio of Electron Densities:**
- The ratio of the maximum electron densities \( \frac{n_{max}}{n_{max}'} \) can be expressed as:
\[ \frac{n_{max}}{n_{max}'} = \frac{(9)^2}{(10)^2} = \frac{81}{100} = 0.81 \]

5. **Conclusion:**
- The rate of maximum electron densities of the ionosphere on the two days is 0.81.