If the wavelength of light is `4000 Å`, then the number of waves in `1 mm` length will be

Options

A. `25`
B. `0.25`
C. `2.5`
D. `25 xx 10^(4)`

Explanation

To solve the problem of finding the number of waves in a length of 1 mm when the wavelength of light is 4000 Å, we can follow these steps:

### Step-by-Step Solution:

1. **Convert Wavelength to Meters**:
The given wavelength is \(4000 \, \text{Å}\) (Angstroms). We need to convert this to meters.
\[ 1 \, \text{Å} = 10^{-10} \, \text{m} \]
Therefore,
\[ 4000 \, \text{Å} = 4000 \times 10^{-10} \, \text{m} = 4 \times 10^{-7} \, \text{m} \]

2. **Convert Length to Meters**:
The length given is \(1 \, \text{mm}\). We also convert this to meters.
\[ 1 \, \text{mm} = 10^{-3} \, \text{m} \]

3. **Calculate the Number of Waves**:
The number of waves (\(n\)) in a length of \(1 \, \text{mm}\) can be calculated using the formula:
\[ n = \frac{\text{Length}}{\text{Wavelength}} = \frac{1 \, \text{mm}}{4000 \, \text{Å}} \]
Substituting the values we converted:
\[ n = \frac{10^{-3} \, \text{m}}{4 \times 10^{-7} \, \text{m}} = \frac{10^{-3}}{4 \times 10^{-7}} \]

4. **Simplify the Calculation**:
Simplifying the fraction:
\[ n = \frac{10^{-3}}{4 \times 10^{-7}} = \frac{10^{-3} \times 10^{7}}{4} = \frac{10^{4}}{4} = 2500 \]

5. **Final Result**:
Therefore, the number of waves in \(1 \, \text{mm}\) length is:
\[ n = 2500 \]