Assertion (A) : Resolving power of electron microscope increases as electron is accelerated through higher voltage.
Reason (R ): de -Broglie wavelength of electron decreases as accelerating voltage of electron increases.

Options

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

Explanation

To solve the question, we need to analyze both the assertion (A) and the reason (R) provided.

### Step 1: Understanding the Assertion (A)
The assertion states that the resolving power of an electron microscope increases as the electron is accelerated through a higher voltage.

### Step 2: Understanding the Reason (R)
The reason states that the de Broglie wavelength of the electron decreases as the accelerating voltage of the electron increases.

### Step 3: Relating the Concepts
1. **De Broglie Wavelength**: The de Broglie wavelength (λ) of an electron can be expressed as:
\[ \lambda = \frac{h}{p} \]
where \(h\) is Planck's constant and \(p\) is the momentum of the electron.

2. **Momentum and Kinetic Energy**: The momentum \(p\) of the electron can be related to its kinetic energy (KE) as:
\[ p = \sqrt{2m \cdot KE} \]
where \(m\) is the mass of the electron and \(KE = eV\) (with \(e\) being the charge of the electron and \(V\) the accelerating voltage).

3. **Substituting Kinetic Energy**: Substituting \(KE\) into the de Broglie wavelength equation gives:
\[ \lambda = \frac{h}{\sqrt{2m \cdot eV}} \]
This shows that as the voltage \(V\) increases, the de Broglie wavelength \(\lambda\) decreases.

### Step 4: Resolving Power of the Microscope
The resolving power (RP) of a microscope is given by:
\[ RP \propto \frac{1}{\lambda} \]
From the relationship derived above, since \(\lambda\) decreases with increasing \(V\), it follows that the resolving power increases with increasing voltage.

### Step 5: Conclusion
Both the assertion and the reason are true:
- The assertion is true because the resolving power increases with higher voltage.
- The reason is true because the de Broglie wavelength decreases with higher voltage.
- The reason correctly explains the assertion.

Thus, the final conclusion is:
- Both A and R are true, and R is the correct explanation of A.

### Final Answer:
Both Assertion (A) and Reason (R) are true, and R is the correct explanation of A.

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