Visible spectrum contains light of following colours ''Violet - Indigo - Blue - Green - Yellow - Orange - Red'' (VIBGYOR).
Its frequency ranges from violet `(7.5xx10^(14) Hz)` to re `(4xx10^(14) Hz.)` Find out the maximum wavelength `("in" "Å")` in this range.

Answer

To find the maximum wavelength in the visible spectrum, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Relationship Between Wavelength and Frequency**:
The relationship between wavelength (λ) and frequency (ν) is given by the equation:
\[ c = \lambda \cdot \nu \]
where \( c \) is the speed of light (approximately \( 3 \times 10^8 \, \text{m/s} \)).

2. **Identify the Frequency Range**:
The frequency range for the visible spectrum is given as:
- Violet: \( 7.5 \times 10^{14} \, \text{Hz} \)
- Red: \( 4 \times 10^{14} \, \text{Hz} \)

To find the maximum wavelength, we need to use the minimum frequency, which corresponds to red light.

3. **Use the Minimum Frequency to Calculate Wavelength**:
We will use the frequency of red light (the lowest frequency in the visible spectrum):
\[ \nu = 4 \times 10^{14} \, \text{Hz} \]
Now, rearranging the formula \( c = \lambda \cdot \nu \) gives us:
\[ \lambda = \frac{c}{\nu} \]

4. **Substitute the Values**:
Substitute the values into the equation:
\[ \lambda = \frac{3 \times 10^8 \, \text{m/s}}{4 \times 10^{14} \, \text{Hz}} \]

5. **Calculate the Wavelength**:
Performing the calculation:
\[ \lambda = \frac{3 \times 10^8}{4 \times 10^{14}} = 7.5 \times 10^{-7} \, \text{m} \]

6. **Convert Meters to Angstroms**:
Since \( 1 \, \text{Å} = 10^{-10} \, \text{m} \), we convert the wavelength from meters to angstroms:
\[ \lambda = 7.5 \times 10^{-7} \, \text{m} \times \frac{10^{10} \, \text{Å}}{1 \, \text{m}} = 7500 \, \text{Å} \]

### Final Answer:
The maximum wavelength in the visible spectrum is \( 7500 \, \text{Å} \).

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