In the question number 48, the energy of photon in eV at the red of the visible spectrum is

Options

A. 6.63
B. 3.62
C. 7.61
D. 1.64

Explanation

To find the energy of a photon at the red end of the visible spectrum, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Wavelength**:
The wavelength of red light at the end of the visible spectrum is approximately 760 nm (nanometers). We need to convert this to meters for our calculations.
\[ \lambda = 760 \, \text{nm} = 760 \times 10^{-9} \, \text{m} = 7.6 \times 10^{-7} \, \text{m} \]

2. **Use the Energy Formula**:
The energy \(E\) of a photon can be calculated using the formula:
\[ E = \frac{hc}{\lambda} \]
where:
- \(h\) is Planck's constant (\(6.63 \times 10^{-34} \, \text{J s}\)),
- \(c\) is the speed of light (\(3 \times 10^{8} \, \text{m/s}\)),
- \(\lambda\) is the wavelength in meters.

3. **Substitute Values**:
Now, substitute the values into the formula:
\[ E = \frac{(6.63 \times 10^{-34} \, \text{J s}) \times (3 \times 10^{8} \, \text{m/s})}{7.6 \times 10^{-7} \, \text{m}} \]

4. **Calculate Energy in Joules**:
Performing the calculation:
\[ E = \frac{1.989 \times 10^{-25} \, \text{J m}}{7.6 \times 10^{-7} \, \text{m}} \approx 2.62 \times 10^{-19} \, \text{J} \]

5. **Convert Joules to Electron Volts**:
To convert the energy from joules to electron volts, use the conversion factor \(1 \, \text{eV} = 1.6 \times 10^{-19} \, \text{J}\):
\[ E \, (\text{in eV}) = \frac{2.62 \times 10^{-19} \, \text{J}}{1.6 \times 10^{-19} \, \text{J/eV}} \approx 1.64 \, \text{eV} \]

6. **Final Answer**:
The energy of a photon at the red end of the visible spectrum is approximately:
\[ \boxed{1.64 \, \text{eV}} \]