The frequency range of visible light is from `3.75 xx 10^(14) Hz to 7.5 xx 10^(14)` Hz. Calculate its wavelength range. Take speed of light = `3 xx 10^(-8) m s^(- l)`

Answer

To solve the problem of calculating the wavelength range of visible light given its frequency range, we can follow these steps:

### Step 1: Understand the relationship between speed, frequency, and wavelength
The relationship is given by the formula:
\[ c = f \times \lambda \]
where:
- \( c \) is the speed of light,
- \( f \) is the frequency,
- \( \lambda \) is the wavelength.

### Step 2: Rearrange the formula to find wavelength
We can rearrange the formula to solve for wavelength:
\[ \lambda = \frac{c}{f} \]

### Step 3: Substitute the values for the lower frequency
The lower frequency of visible light is given as \( f_1 = 3.75 \times 10^{14} \) Hz. The speed of light is given as \( c = 3 \times 10^8 \) m/s. Now, we can calculate the wavelength corresponding to this frequency:
\[ \lambda_1 = \frac{3 \times 10^8 \text{ m/s}}{3.75 \times 10^{14} \text{ Hz}} \]
Calculating this gives:
\[ \lambda_1 = \frac{3 \times 10^8}{3.75 \times 10^{14}} = 8 \times 10^{-7} \text{ m} \]

### Step 4: Convert the wavelength to nanometers
To convert meters to nanometers, we multiply by \( 10^9 \):
\[ \lambda_1 = 8 \times 10^{-7} \text{ m} \times 10^9 \text{ nm/m} = 800 \text{ nm} \]

### Step 5: Substitute the values for the upper frequency
Now, we calculate the wavelength for the upper frequency \( f_2 = 7.5 \times 10^{14} \) Hz:
\[ \lambda_2 = \frac{3 \times 10^8 \text{ m/s}}{7.5 \times 10^{14} \text{ Hz}} \]
Calculating this gives:
\[ \lambda_2 = \frac{3 \times 10^8}{7.5 \times 10^{14}} = 4 \times 10^{-7} \text{ m} \]

### Step 6: Convert the second wavelength to nanometers
Again, converting to nanometers:
\[ \lambda_2 = 4 \times 10^{-7} \text{ m} \times 10^9 \text{ nm/m} = 400 \text{ nm} \]

### Step 7: State the wavelength range
The wavelength range of visible light is therefore from \( 400 \text{ nm} \) to \( 800 \text{ nm} \).

### Final Answer:
The wavelength range of visible light is from **400 nm to 800 nm**.

---