Which of the following represents an infrared wavelength

Options

A. `10^(-4) cm`
B. `10^(-5) cm`
C. `10^(-8) cm`
D. `10^(-7) cm`

Answer

To determine which of the given options represents an infrared wavelength, we can follow these steps:

### Step 1: Understand the Wavelength Range of Infrared Radiation
Infrared radiation (IR) is part of the electromagnetic spectrum. The typical wavelength range for infrared radiation is from 700 nanometers (nm) to 1 millimeter (mm).

### Step 2: Convert the Wavelength Range to Centimeters
1 nanometer is equal to \(10^{-9}\) meters, and 1 millimeter is equal to \(10^{-3}\) meters. To convert nanometers and millimeters to centimeters:
- 700 nm = \(700 \times 10^{-9}\) m = \(7 \times 10^{-7}\) m = \(7 \times 10^{-5}\) cm
- 1 mm = \(1 \times 10^{-3}\) m = \(0.1\) cm

Thus, the infrared wavelength range in centimeters is from \(7 \times 10^{-5}\) cm to \(0.1\) cm.

### Step 3: Analyze the Given Options
Now let's look at the options provided:
1. Option 1: \(10^{-4}\) cm
2. Option 2: \(10^{-5}\) cm
3. Option 3: \(10^{-8}\) cm
4. Option 4: \(10^{-7}\) cm

### Step 4: Determine Which Option Falls Within the Infrared Range
- \(10^{-4}\) cm = \(0.0001\) cm (which is \(1 \times 10^{-6}\) m or \(1000\) nm)
- \(10^{-5}\) cm = \(0.00001\) cm (which is \(100\) nm)
- \(10^{-8}\) cm = \(0.00000001\) cm (which is \(0.01\) nm)
- \(10^{-7}\) cm = \(0.0000001\) cm (which is \(0.1\) nm)

From the converted values, we can see that:
- \(10^{-4}\) cm (1000 nm) is within the infrared range (700 nm to 1 mm).
- The other options (\(10^{-5}\), \(10^{-8}\), and \(10^{-7}\) cm) are outside the infrared range.

### Conclusion
The correct answer is **Option 1: \(10^{-4}\) cm**, as it falls within the infrared wavelength range.

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