Assertion: The de Broglie wavelength of an electron in `n^(th)` Bohr orbit of hydrogen is inversely proportional to the square of quantum number n.
Reason: The magnitude of angular momentum of an electron in `n^(th)` Bohr orbit of hydrogen atom is directly proportional to n.

Options

A. If both assertion and reason are correct and reason is a correct explanation of the assertion.
B. If both assertion and reason are correct but is not the correct explanation of assertion.
C. If assertion is correct but reason is incorrect.
D. If assertion is incorrect but reason is correct.

Explanation

To solve the question, we need to analyze both the assertion and the reason provided.

### Step 1: Understand the Assertion
The assertion states that the de Broglie wavelength of an electron in the nth Bohr orbit of hydrogen is inversely proportional to the square of the quantum number n.

**De Broglie Wavelength Formula:**
The de Broglie wavelength (λ) is given by the formula:
\[ \lambda = \frac{h}{mv} \]
where:
- \( h \) is Planck's constant,
- \( m \) is the mass of the electron,
- \( v \) is the velocity of the electron.

### Step 2: Analyze the Velocity of the Electron
From Bohr's model, the velocity of an electron in the nth orbit can be expressed as:
\[ v_n \propto \frac{1}{n} \]
This means that as n increases, the velocity decreases inversely.

### Step 3: Substitute the Velocity into the Wavelength Formula
Substituting \( v_n \) into the de Broglie wavelength equation gives:
\[ \lambda_n = \frac{h}{m \cdot v_n} \propto \frac{h}{m \cdot \frac{1}{n}} \propto n \]
This shows that the de Broglie wavelength is directly proportional to n, not inversely proportional to \( n^2 \).

### Step 4: Understand the Reason
The reason states that the magnitude of angular momentum of an electron in the nth Bohr orbit is directly proportional to n.

**Angular Momentum in Bohr's Model:**
According to Bohr's postulates:
\[ L_n = n \frac{h}{2\pi} \]
This shows that the angular momentum (L) is indeed directly proportional to n.

### Step 5: Conclusion
- The assertion is incorrect because the de Broglie wavelength is directly proportional to n, not inversely proportional to \( n^2 \).
- The reason is correct as the angular momentum is directly proportional to n.

Thus, the correct answer is: **Assertion is incorrect, and Reason is correct.**