The wavelength of light in the visible region is about 390 nm for violet colour and about 760 nm for red colour. The energy of photon in eV at violet end is

Options

A. 2.32
B. 3.19
C. 1.42
D. 4.13

Explanation

To calculate the energy of a photon at the violet end of the visible spectrum (wavelength = 390 nm), we can use the formula that relates energy, wavelength, and the speed of light. Here’s a step-by-step solution:

### Step 1: Convert the wavelength from nanometers to meters
The given wavelength for violet light is 390 nm.
1 nm = \(10^{-9}\) m, so:
\[ \text{Wavelength} (\lambda) = 390 \, \text{nm} = 390 \times 10^{-9} \, \text{m} \]

### Step 2: Use the formula for energy of a photon
The energy (E) of a photon can be calculated using the formula:
\[ E = \frac{hc}{\lambda} \]
where:
- \(h\) is Planck's constant (\(6.626 \times 10^{-34} \, \text{J s}\)),
- \(c\) is the speed of light (\(3 \times 10^8 \, \text{m/s}\)),
- \(\lambda\) is the wavelength in meters.

### Step 3: Substitute the values into the formula
Substituting the values we have:
\[ E = \frac{(6.626 \times 10^{-34} \, \text{J s}) \times (3 \times 10^8 \, \text{m/s})}{390 \times 10^{-9} \, \text{m}} \]

### Step 4: Calculate the energy in joules
Calculating the numerator:
\[ E = \frac{(6.626 \times 3) \times 10^{-34 + 8}}{390 \times 10^{-9}} \]
Calculating \(6.626 \times 3 = 19.878\):
\[ E = \frac{19.878 \times 10^{-26}}{390 \times 10^{-9}} = \frac{19.878}{390} \times 10^{-26 + 9} \]
Calculating \(19.878 / 390 \approx 0.051\):
\[ E \approx 0.051 \times 10^{-17} = 5.1 \times 10^{-19} \, \text{J} \]

### Step 5: Convert the energy from joules to electron volts
To convert joules to electron volts, we use the conversion factor \(1 \, \text{eV} = 1.6 \times 10^{-19} \, \text{J}\):
\[ E \text{ (in eV)} = \frac{5.1 \times 10^{-19} \, \text{J}}{1.6 \times 10^{-19} \, \text{J/eV}} \approx 3.19 \, \text{eV} \]

### Final Answer
The energy of a photon at the violet end (390 nm) is approximately **3.19 eV**.

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