Given below are two statements : one is labelled as Assertion A and the other is labelled as
Assertion A: An electron microscope can achieve better resolving power than an optical microscope.
Reason R : The de Broglie's wavelength of the electrons emitted from an electron gun is much less than wavelength of visible light. In the light of the above statements, choose the correct answer from the options given below:

Options

A. A is true but R is false.
B. Both A and R are true and R is the correct explanation of A.
C. Both A and R are true but R is NOT the correct explanation of A.
D. A is false but Ris true.

Answer

To solve the problem, we need to analyze the two statements provided: Assertion A and Reason R.

### Step 1: Analyze Assertion A
Assertion A states that "An electron microscope can achieve better resolving power than an optical microscope."

- **Resolving Power**: The resolving power of an optical instrument is its ability to distinguish between two closely spaced objects. The resolving power (RP) is inversely related to the wavelength (λ) of the light used. The formula is given by:
\[ RP \propto \frac{1}{\lambda} \]
- **Comparison**: Electron microscopes use electrons, which have much shorter wavelengths compared to visible light used in optical microscopes. Therefore, since the wavelength of electrons is significantly smaller, the resolving power of an electron microscope is indeed greater than that of an optical microscope.

**Conclusion for Step 1**: Assertion A is true.

### Step 2: Analyze Reason R
Reason R states that "The de Broglie's wavelength of the electrons emitted from an electron gun is much less than the wavelength of visible light."

- **De Broglie's Wavelength**: The de Broglie wavelength (λ) 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. For electrons, which are accelerated in an electron gun, the resulting wavelength is much smaller than that of visible light.
- **Comparison with Visible Light**: The wavelength of visible light ranges from approximately 400 nm to 700 nm, while the de Broglie wavelength of electrons can be in the order of picometers (10^-12 m), which is significantly less than that of visible light.

**Conclusion for Step 2**: Reason R is true.

### Step 3: Determine the Relationship Between A and R
Now we need to determine if Reason R correctly explains Assertion A.

- Since Assertion A is true and Reason R provides a valid explanation for why electron microscopes have better resolving power (due to the shorter wavelength of electrons), we can conclude that both statements are true and that Reason R correctly explains Assertion A.

### Final Conclusion
Both Assertion A and Reason R are true, and Reason R is the correct explanation for Assertion A.

### Answer: Option B (Both A and R are true, and R is the correct explanation of A)

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