The photon energy, in eV, for electromagnetic waves of wavelength 40 m is

Options

A. `3.1 xx 10^(-5)`
B. `4.8 xx 10^(-27)`
C. `6.2 xx 10^(-8)`
D. `9.6 xx 10^(-27)`

Explanation

To calculate the photon energy for electromagnetic waves of wavelength 40 m, we can use the formula for energy of a photon:

### Step-by-Step Solution:

1. **Identify the formula for photon energy**:
The energy \( E \) of a photon can be calculated using the formula:
\[ E = \frac{hc}{\lambda} \]
where:
- \( E \) = energy of the photon (in Joules)
- \( h \) = Planck's constant \( \approx 6.626 \times 10^{-34} \, \text{J s} \)
- \( c \) = speed of light \( \approx 3.00 \times 10^{8} \, \text{m/s} \)
- \( \lambda \) = wavelength (in meters)

2. **Substitute the given values**:
Given that the wavelength \( \lambda = 40 \, \text{m} \), we can substitute the values into the formula:
\[ E = \frac{(6.626 \times 10^{-34} \, \text{J s}) \times (3.00 \times 10^{8} \, \text{m/s})}{40 \, \text{m}} \]

3. **Calculate the energy in Joules**:
Performing the calculation:
\[ E = \frac{(6.626 \times 10^{-34}) \times (3.00 \times 10^{8})}{40} \]
\[ E = \frac{1.9878 \times 10^{-25}}{40} = 4.9695 \times 10^{-27} \, \text{J} \]

4. **Convert the energy from Joules to electron volts**:
To convert Joules to electron volts, we use the conversion factor \( 1 \, \text{eV} = 1.6 \times 10^{-19} \, \text{J} \):
\[ E \, (\text{in eV}) = \frac{4.9695 \times 10^{-27} \, \text{J}}{1.6 \times 10^{-19} \, \text{J/eV}} \]
\[ E \, (\text{in eV}) = 3.1059 \times 10^{-8} \, \text{eV} \]

5. **Final result**:
The photon energy for electromagnetic waves of wavelength 40 m is approximately:
\[ E \approx 3.1 \times 10^{-8} \, \text{eV} \]