Wavelength of a `1 ke V` photon is `1.24 xx 10^(-9) m`. What is the frequency of ` 1 Me V` photon ?

Options

A. `1.24 xx 10^(15)`Hz
B. `2.5 xx 10^(20) Hz`
C. `1.24 xx 10^(18)` Hz
D. `2.4 xx 10^(23)`Hz

Answer

To find the frequency of a `1 MeV` photon, we can use the relationship between energy, frequency, and wavelength. The energy of a photon can be expressed in two ways:

1. \( E = \frac{hc}{\lambda} \)
2. \( E = h\nu \)

Where:
- \( E \) is the energy of the photon,
- \( h \) is Planck's constant (\( 6.626 \times 10^{-34} \, \text{Js} \)),
- \( c \) is the speed of light (\( 3 \times 10^8 \, \text{m/s} \)),
- \( \lambda \) is the wavelength,
- \( \nu \) is the frequency.

### Step-by-Step Solution:

1. **Convert Energy Units**:
- We know that \( 1 \, \text{MeV} = 10^6 \, \text{eV} \).
- Therefore, the energy of a `1 MeV` photon is \( E = 10^6 \, \text{eV} \).

2. **Use the Energy-Frequency Relationship**:
- From the equation \( E = h\nu \), we can express frequency as:
\[ \nu = \frac{E}{h} \]
- We need to convert the energy from electron volts to joules. The conversion factor is:
\[ 1 \, \text{eV} = 1.6 \times 10^{-19} \, \text{J} \]
- Thus, \( E = 10^6 \, \text{eV} = 10^6 \times 1.6 \times 10^{-19} \, \text{J} = 1.6 \times 10^{-13} \, \text{J} \).

3. **Substitute Values into the Frequency Equation**:
- Now we can substitute \( E \) and \( h \) into the frequency equation:
\[ \nu = \frac{1.6 \times 10^{-13} \, \text{J}}{6.626 \times 10^{-34} \, \text{Js}} \]

4. **Calculate the Frequency**:
- Performing the calculation:
\[ \nu = \frac{1.6 \times 10^{-13}}{6.626 \times 10^{-34}} \approx 2.41 \times 10^{20} \, \text{Hz} \]

5. **Final Result**:
- The frequency of a `1 MeV` photon is approximately \( 2.41 \times 10^{20} \, \text{Hz} \).