Calculate the frequency of infrared radiations having wavelength, `3 xx 10^(6)nm`.

Explanation

To calculate the frequency of infrared radiation with a given wavelength, we can use the formula:

\[ f = \frac{c}{\lambda} \]

where:
- \( f \) is the frequency,
- \( c \) is the speed of light (approximately \( 3 \times 10^8 \) m/s),
- \( \lambda \) is the wavelength.

### Step-by-Step Solution:

1. **Convert Wavelength from Nanometers to Meters:**
The wavelength is given as \( 3 \times 10^6 \) nm. We need to convert this to meters.
\[ 1 \text{ nm} = 10^{-9} \text{ m} \]
Therefore,
\[ \lambda = 3 \times 10^6 \text{ nm} = 3 \times 10^6 \times 10^{-9} \text{ m} = 3 \times 10^{-3} \text{ m} \]

**Hint:** Remember to convert nanometers to meters using the conversion factor \( 1 \text{ nm} = 10^{-9} \text{ m} \).

2. **Use the Speed of Light:**
The speed of light \( c \) is approximately \( 3 \times 10^8 \) m/s.

3. **Calculate the Frequency:**
Now, substitute the values of \( c \) and \( \lambda \) into the frequency formula:
\[ f = \frac{c}{\lambda} = \frac{3 \times 10^8 \text{ m/s}}{3 \times 10^{-3} \text{ m}} \]

Simplifying this gives:
\[ f = \frac{3 \times 10^8}{3 \times 10^{-3}} = 10^{8 + 3} = 10^{11} \text{ s}^{-1} \]

4. **Final Answer:**
Therefore, the frequency of the infrared radiation is:
\[ f = 10^{11} \text{ Hz} \]

### Summary:
The frequency of infrared radiation with a wavelength of \( 3 \times 10^6 \) nm is \( 10^{11} \) Hz.