A proton and an electron both have energy 50 eV.
Statement I: Both have different wavelength.
Statement II: Wavelength depends on energy and not on mass.

Options

A. Statement I is true, Statement II is true, Statement II is a correct explanation for Statement I
B. Statement I is True, Statement II is True, Statement II is NOT a correct explanation for Statement I
C. Statement I is True, Statement II is False .
D. Statement I is false, Statement II is True.

Explanation

To analyze the statements about the proton and electron with energy 50 eV, we need to understand the relationship between energy, mass, and wavelength.

### Step-by-Step Solution:

1. **Understanding the de Broglie Wavelength**:
The de Broglie wavelength (\( \lambda \)) of a particle is given by the formula:
\[ \lambda = \frac{h}{p} \]
where \( h \) is Planck's constant and \( p \) is the momentum of the particle. The momentum \( p \) can also be expressed in terms of kinetic energy (\( K \)) and mass (\( m \)) as:
\[ p = \sqrt{2mK} \]
Therefore, we can rewrite the wavelength as:
\[ \lambda = \frac{h}{\sqrt{2mK}} \]

2. **Calculating the Wavelength for Proton and Electron**:
Given that both the proton and electron have the same kinetic energy \( K = 50 \, \text{eV} \), we need to consider their masses:
- Mass of proton (\( m_p \)) ≈ \( 1.67 \times 10^{-27} \, \text{kg} \)
- Mass of electron (\( m_e \)) ≈ \( 9.11 \times 10^{-31} \, \text{kg} \)

Since the mass of the proton is much larger than that of the electron, we can conclude that:
\[ \lambda_p = \frac{h}{\sqrt{2m_p \cdot 50 \, \text{eV}}} \]
\[ \lambda_e = \frac{h}{\sqrt{2m_e \cdot 50 \, \text{eV}}} \]

Because \( m_p \) is significantly greater than \( m_e \), \( \lambda_p \) will be much smaller than \( \lambda_e \). Thus, the wavelengths are different.

3. **Evaluating Statement I**:
Statement I claims that both the proton and electron have different wavelengths. Since we have established that the wavelengths depend on both mass and energy, and given that the masses are different, this statement is **correct**.

4. **Evaluating Statement II**:
Statement II claims that wavelength depends on energy and not on mass. However, from the de Broglie wavelength formula, we see that the wavelength does indeed depend on both mass and energy. Therefore, this statement is **incorrect**.

### Conclusion:
- Statement I is correct.
- Statement II is incorrect.

Thus, the answer is that Statement I is correct, and Statement II is not a correct explanation of Statement I.