The de-Broglie wavelength of an electron is same as the wavelength of a photon. The energy of a photon is ‘x’ times the K.E. of the electron, then ‘x’ is: (m-mass of electron, h-Planck’s constant, c - velocity of light)

Options

A. `(hc)/(2lambdam)`
B. `(2lambdamc)/(h)`
C. `(2lambdac)/(hm)`
D. `(2lambdam)(ch)`

Explanation

To solve the problem, we need to establish the relationship between the de-Broglie wavelength of an electron and the wavelength of a photon, and then relate the energies involved.

### Step-by-Step Solution:

1. **Understand the de-Broglie wavelength**:
The de-Broglie wavelength (\(\lambda\)) of an electron is given by the formula:
\[ \lambda = \frac{h}{mv} \]
where \(h\) is Planck's constant, \(m\) is the mass of the electron, and \(v\) is its velocity.

2. **Photon wavelength**:
The wavelength of a photon is also denoted by \(\lambda\) and is related to its energy \(E\) by the equation:
\[ E = \frac{hc}{\lambda} \]
where \(c\) is the speed of light.

3. **Kinetic energy of the electron**:
The kinetic energy (K.E.) of the electron can be expressed as:
\[ K.E. = \frac{1}{2} mv^2 \]

4. **Relate the energies**:
According to the problem, the energy of the photon is \(x\) times the kinetic energy of the electron:
\[ E_{photon} = x \cdot K.E. \]
Substituting the expressions for energy, we have:
\[ \frac{hc}{\lambda} = x \cdot \frac{1}{2} mv^2 \]

5. **Substituting the velocity**:
From the de-Broglie wavelength equation, we can express \(v\) in terms of \(\lambda\):
\[ v = \frac{h}{m\lambda} \]
Now substituting this \(v\) into the kinetic energy equation:
\[ K.E. = \frac{1}{2} m \left(\frac{h}{m\lambda}\right)^2 = \frac{h^2}{2m\lambda^2} \]

6. **Substituting K.E. back into the energy equation**:
Now substituting \(K.E.\) back into the energy equation:
\[ \frac{hc}{\lambda} = x \cdot \frac{h^2}{2m\lambda^2} \]

7. **Rearranging the equation**:
Multiply both sides by \(2m\lambda^2\):
\[ 2m\lambda \cdot hc = x \cdot h^2 \]
Now, divide both sides by \(h\):
\[ 2m\lambda c = x \cdot h \]

8. **Solving for \(x\)**:
Finally, rearranging gives:
\[ x = \frac{2m\lambda c}{h} \]

### Conclusion:
Thus, the value of \(x\) is:
\[ x = \frac{2m\lambda c}{h} \]