Statement-1:An electron microscope can achieve better resolving power than an optical microscope
Statement-2:The de Broglie wavelength of the electrons emitted from an electron gun is much less than 500 nm

Options

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

Answer

To solve the question, we need to analyze both statements and determine their validity and relationship.

### Step 1: Analyze Statement 1
**Statement 1:** An electron microscope can achieve better resolving power than an optical microscope.

- **Explanation:** The resolving power of a microscope is determined by the wavelength of the particles used for imaging. An electron microscope uses electrons, which have a much smaller wavelength compared to visible light (photons) used in optical microscopes. The resolving power improves as the wavelength decreases.

### Step 2: Analyze Statement 2
**Statement 2:** The de Broglie wavelength of the electrons emitted from an electron gun is much less than 500 nm.

- **Explanation:** The de Broglie wavelength (λ) of a particle is given by the formula:
\[ λ = \frac{h}{p} \]
where \( h \) is Planck's constant and \( p \) is the momentum of the particle. Electrons emitted from an electron gun typically have high kinetic energy, resulting in a very small de Broglie wavelength, often much less than 500 nm. This supports the assertion in Statement 1.

### Step 3: Conclusion
Both statements are true, and Statement 2 provides a correct explanation for Statement 1. Therefore, the correct answer is:
- **Option A:** Statement 1 is true, Statement 2 is true, and Statement 2 is a correct explanation of Statement 1.

### Final Answer:
**Option A:** Statement 1 is true, Statement 2 is true, and Statement 2 is a correct explanation of Statement 1.

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