Calculate the frequency corresponding to the wavelength `4000 Å`

Explanation

To calculate the frequency corresponding to the wavelength of 4000 Å (angstroms), we can follow these steps:

### Step 1: Convert Wavelength from Angstroms to Meters
The wavelength is given as 4000 Å. We need to convert this to meters.

1 Å = \(10^{-10}\) meters, so:
\[ 4000 \, \text{Å} = 4000 \times 10^{-10} \, \text{meters} = 4.0 \times 10^{-7} \, \text{meters} \]

### Step 2: Use the Formula for Frequency
The frequency (\( \nu \)) can be calculated using the formula:
\[ \nu = \frac{c}{\lambda} \]
where:
- \( c \) is the speed of light, approximately \( 3 \times 10^{8} \, \text{m/s} \)
- \( \lambda \) is the wavelength in meters

### Step 3: Substitute the Values into the Formula
Now, substituting the values into the formula:
\[ \nu = \frac{3 \times 10^{8} \, \text{m/s}}{4.0 \times 10^{-7} \, \text{m}} \]

### Step 4: Perform the Calculation
Now, we perform the division:
\[ \nu = \frac{3 \times 10^{8}}{4.0 \times 10^{-7}} = 7.5 \times 10^{14} \, \text{s}^{-1} \]

### Step 5: Convert to Hertz
Since \( 1 \, \text{s}^{-1} \) is equivalent to 1 Hz, we can express the frequency as:
\[ \nu = 7.5 \times 10^{14} \, \text{Hz} \]

### Final Answer
The frequency corresponding to the wavelength of 4000 Å is:
\[ \nu = 7.5 \times 10^{14} \, \text{Hz} \]

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