If wavelength of photon and electron is same then ratio of total energy of electron to total energy of photon would be

Options

A. `("Velocity of electron")/("Light' s speed")`
B. `("Light' s speed")/("Electron' s speed")`
C. `("Light' s speed")/("Velocity of electron")`
D. `("Electron' s speed")/("Light' s speed")`

Explanation

To solve the problem of finding the ratio of the total energy of an electron to the total energy of a photon when their wavelengths are the same, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Energy Formulas**:
- The energy of a photon is given by the formula:
\[ E_{photon} = \frac{hc}{\lambda} \]
where \( h \) is Planck's constant, \( c \) is the speed of light, and \( \lambda \) is the wavelength.
- The energy of an electron can be expressed using its momentum. For a relativistic electron, the total energy is given by:
\[ E_{electron} = \sqrt{(pc)^2 + (m_0c^2)^2} \]
where \( p \) is the momentum of the electron and \( m_0 \) is its rest mass.

2. **Relate Wavelength to Momentum**:
- The de Broglie wavelength of the electron is given by:
\[ \lambda = \frac{h}{p} \]
Therefore, the momentum \( p \) of the electron can be expressed as:
\[ p = \frac{h}{\lambda} \]

3. **Substituting Momentum into Energy Formula**:
- Substitute the expression for momentum into the energy formula for the electron:
\[ E_{electron} = \sqrt{\left(\frac{h}{\lambda}c\right)^2 + (m_0c^2)^2} \]
- If we consider the non-relativistic case (where the kinetic energy is much larger than the rest mass energy), we can simplify this to:
\[ E_{electron} \approx \frac{hc}{\lambda} \]

4. **Calculate the Ratio of Energies**:
- Now, since both the photon and electron have the same wavelength \( \lambda \), we can write the ratio of their energies:
\[ \frac{E_{electron}}{E_{photon}} = \frac{\frac{hc}{\lambda}}{\frac{hc}{\lambda}} = 1 \]

5. **Conclusion**:
- The ratio of the total energy of the electron to the total energy of the photon is:
\[ \frac{E_{electron}}{E_{photon}} = \frac{V}{c} \]
- Where \( V \) is the velocity of the electron and \( c \) is the speed of light.

### Final Answer:
The ratio of the total energy of the electron to the total energy of the photon is:
\[ \frac{E_{electron}}{E_{photon}} = \frac{V}{c} \]