Wavelength of photon is equal to the wavelength of electron moving with kinetic energy 1.5 eV. What is the value of energy of photon :

Options

A. 12.25 eV
B. 1.24 eV
C. 1.5 eV
D. 1.24 KeV

Explanation

To solve the problem, we need to find the energy of a photon whose wavelength is equal to that of an electron moving with a kinetic energy of 1.5 eV.

### Step-by-Step Solution:

1. **Determine the wavelength of the electron**:
The wavelength (λ) of an electron can be calculated using the formula:
\[ \lambda = \frac{12.27}{\sqrt{K.E.}} \]
where K.E. is the kinetic energy in electron volts (eV). Given that the kinetic energy of the electron is 1.5 eV, we can substitute this value into the formula:
\[ \lambda = \frac{12.27}{\sqrt{1.5}} \]

2. **Calculate the wavelength**:
First, we need to calculate \(\sqrt{1.5}\):
\[ \sqrt{1.5} \approx 1.2247 \]
Now substituting this back into the wavelength formula:
\[ \lambda = \frac{12.27}{1.2247} \approx 10.02 \text{ Å (angstroms)} \]

3. **Use the wavelength to find the energy of the photon**:
The energy (E) of a photon can be calculated using the formula:
\[ E = \frac{12400}{\lambda} \]
where λ is in angstroms. Now substituting the value of λ we found:
\[ E = \frac{12400}{10.02} \]

4. **Calculate the energy**:
Performing the calculation:
\[ E \approx 1239.68 \text{ eV} \]

5. **Final Result**:
The energy of the photon is approximately 1239.68 eV.