STATEMENT-1 `:` The de-Broglie wavelength of an electron decreases as kinetic energy decreases.
and
STATEMENT- 2 `:` The de-Broglie wavelength `lambda= ( h)/(sqrt( 2mKE))`

Options

A. Statement-1 is True, Statement-2 is True, Statement-2 is a correct explanation for Statement-1
B. Statement-1 is True, Statement-2 isTrue, Statement-2 is NOT a correct explanation for Statement-1
C. Statement-1 is True, Statement-2 is False
D. Statement-1 is False , Statement-2 isTrue

Answer

To solve the question, we need to analyze both statements regarding the de-Broglie wavelength of an electron and its relationship with kinetic energy.

### Step-by-Step Solution:

1. **Understanding de-Broglie Wavelength**:
The de-Broglie wavelength (\( \lambda \)) of a particle is given by the formula:
\[ \lambda = \frac{h}{\sqrt{2m \cdot KE}} \]
where:
- \( h \) is Planck's constant,
- \( m \) is the mass of the particle (electron in this case),
- \( KE \) is the kinetic energy of the particle.

2. **Analyzing Statement 1**:
Statement 1 claims that "the de-Broglie wavelength of an electron decreases as kinetic energy decreases." To analyze this, we can rearrange the formula:
- As \( KE \) decreases, the term \( \sqrt{2m \cdot KE} \) in the denominator decreases.
- Since \( \lambda \) is inversely proportional to \( \sqrt{2m \cdot KE} \), a decrease in \( KE \) leads to an increase in \( \lambda \).
- Therefore, Statement 1 is **incorrect**.

3. **Analyzing Statement 2**:
Statement 2 states the formula for the de-Broglie wavelength:
\[ \lambda = \frac{h}{\sqrt{2m \cdot KE}} \]
This statement is a correct representation of the relationship between the de-Broglie wavelength and kinetic energy.

4. **Conclusion**:
- Since Statement 1 is incorrect and Statement 2 is correct, we conclude that the correct answer is that Statement 1 is false and Statement 2 is true.

### Final Answer:
- **Statement 1 is false.**
- **Statement 2 is true.**