Speed of light in vacuum is `3xx10^(8) m//s`. Range of wavelength of visible light is `4000Å -7000Å`. Find the range of frequency of visible light.

Explanation

To find the range of frequency of visible light given the speed of light in vacuum and the range of wavelengths, we can follow these steps:

### Step 1: Understand the relationship between speed, frequency, and wavelength
The relationship between the speed of light (V), frequency (f), and wavelength (λ) is given by the formula:
\[ V = f \times \lambda \]
From this, we can express frequency as:
\[ f = \frac{V}{\lambda} \]

### Step 2: Convert the wavelength from Angstroms to meters
We know that:
\[ 1 \text{ Å} = 10^{-10} \text{ m} \]
Thus, we convert the given wavelengths:
- Maximum wavelength (λ_max) = 7000 Å = \( 7000 \times 10^{-10} \text{ m} \)
- Minimum wavelength (λ_min) = 4000 Å = \( 4000 \times 10^{-10} \text{ m} \)

### Step 3: Calculate the minimum frequency (f_min)
To find the minimum frequency, we use the maximum wavelength:
\[ f_{\text{min}} = \frac{V}{\lambda_{\text{max}}} \]
Substituting the values:
\[ V = 3 \times 10^8 \text{ m/s} \]
\[ \lambda_{\text{max}} = 7000 \times 10^{-10} \text{ m} \]
Now, calculate:
\[ f_{\text{min}} = \frac{3 \times 10^8}{7000 \times 10^{-10}} \]
\[ f_{\text{min}} = \frac{3 \times 10^8}{7 \times 10^{-7}} \]
\[ f_{\text{min}} = \frac{3}{7} \times 10^{15} \]
\[ f_{\text{min}} \approx 4.29 \times 10^{14} \text{ Hz} \]

### Step 4: Calculate the maximum frequency (f_max)
To find the maximum frequency, we use the minimum wavelength:
\[ f_{\text{max}} = \frac{V}{\lambda_{\text{min}}} \]
Substituting the values:
\[ \lambda_{\text{min}} = 4000 \times 10^{-10} \text{ m} \]
Now, calculate:
\[ f_{\text{max}} = \frac{3 \times 10^8}{4000 \times 10^{-10}} \]
\[ f_{\text{max}} = \frac{3 \times 10^8}{4 \times 10^{-7}} \]
\[ f_{\text{max}} = \frac{3}{4} \times 10^{15} \]
\[ f_{\text{max}} \approx 7.5 \times 10^{14} \text{ Hz} \]

### Step 5: State the range of frequency
The range of frequency of visible light is:
\[ f_{\text{min}} \approx 4.29 \times 10^{14} \text{ Hz} \]
\[ f_{\text{max}} \approx 7.5 \times 10^{14} \text{ Hz} \]
Thus, the required range of frequency is:
\[ 4.29 \times 10^{14} \text{ Hz} \text{ to } 7.5 \times 10^{14} \text{ Hz} \]