The wavelength of electromagnetic waves employed for space communication lie in the the range of-

Options

A. 1mm to 30 m
B. 1 mm to 300 m
C. 1 mm to 3 km
D. 1mm to 30 km

Answer

To determine the wavelength of electromagnetic waves employed for space communication, we can follow these steps:

### Step 1: Understand the frequency range for space communication.
The frequency range for space communication is given as \(10^4 \, \text{Hz}\) to \(10^{11} \, \text{Hz}\).

### Step 2: Use the relationship between speed, frequency, and wavelength.
The relationship between speed (C), frequency (μ), and wavelength (λ) is given by the formula:
\[ C = \mu \lambda \]
From this, we can rearrange to find the wavelength:
\[ \lambda = \frac{C}{\mu} \]
where \(C\) is the speed of light, approximately \(3 \times 10^8 \, \text{m/s}\).

### Step 3: Calculate the wavelength for the lower frequency limit.
For the lower frequency limit (\(μ_1 = 10^4 \, \text{Hz}\)):
\[ \lambda_1 = \frac{C}{μ_1} = \frac{3 \times 10^8 \, \text{m/s}}{10^4 \, \text{Hz}} = 3 \times 10^4 \, \text{m} = 30 \, \text{km} \]

### Step 4: Calculate the wavelength for the upper frequency limit.
For the upper frequency limit (\(μ_2 = 10^{11} \, \text{Hz}\)):
\[ \lambda_2 = \frac{C}{μ_2} = \frac{3 \times 10^8 \, \text{m/s}}{10^{11} \, \text{Hz}} = 3 \times 10^{-3} \, \text{m} = 3 \, \text{mm} \]

### Step 5: Determine the range of wavelengths.
From the calculations:
- The wavelength for \(10^4 \, \text{Hz}\) is \(30 \, \text{km}\).
- The wavelength for \(10^{11} \, \text{Hz}\) is \(3 \, \text{mm}\).

Thus, the range of wavelengths for electromagnetic waves used in space communication is from \(3 \, \text{mm}\) to \(30 \, \text{km}\).

### Step 6: Identify the correct answer from the options.
The range of wavelengths calculated is \(3 \, \text{mm} \) to \(30 \, \text{km}\), which corresponds to the option \(1 \, \text{mm} \) to \(30 \, \text{km}\). Therefore, the correct answer is option D.

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