Read the following statements and choose the correct option. (I) If the radius of the first Bohr orbit of hydrogen atom is r and of `2^(nd)` orbit of `Li^(2+)` would be 4r. (II) For s-orbital electron , the orbital angular momentum is zero

Options

A. only I is correct
B. only II is correct
C. bothare correct
D. both are incorrect

Answer

To solve the question, we need to analyze the two statements provided and determine their correctness.

### Step 1: Analyze the first statement
The first statement claims that if the radius of the first Bohr orbit of the hydrogen atom is \( r \), then the radius of the second orbit of \( \text{Li}^{2+} \) would be \( 4r \).

1. **Bohr's Radius Formula**: The radius of the \( n \)-th Bohr orbit for hydrogen-like atoms is given by the formula:
\[ r_n = a_0 \frac{n^2}{Z} \]
where \( a_0 \) is the Bohr radius (approximately \( 0.529 \) Å), \( n \) is the principal quantum number, and \( Z \) is the atomic number.

2. **Calculate for Hydrogen**: For hydrogen (\( Z = 1 \)) and the first orbit (\( n = 1 \)):
\[ r_1 = a_0 \frac{1^2}{1} = a_0 = 0.529 \text{ Å} = r \]

3. **Calculate for \( \text{Li}^{2+} \)**: For lithium (\( Z = 3 \)) and the second orbit (\( n = 2 \)):
\[ r_2 = a_0 \frac{2^2}{3} = a_0 \frac{4}{3} = 0.529 \times \frac{4}{3} \approx 0.529 \times 1.33 \approx 0.706 \text{ Å} \]
Since \( r \) (the radius of the first orbit of hydrogen) is \( 0.529 \) Å, we find:
\[ r_2 \approx 1.33r \]
Therefore, the statement that \( r_2 = 4r \) is incorrect.

### Step 2: Analyze the second statement
The second statement claims that for an s-orbital electron, the orbital angular momentum is zero.

1. **Orbital Angular Momentum Formula**: The orbital angular momentum \( L \) is given by:
\[ L = \sqrt{l(l + 1)} \frac{h}{2\pi} \]
where \( l \) is the azimuthal quantum number.

2. **For s-orbital**: For s-orbitals, \( l = 0 \):
\[ L = \sqrt{0(0 + 1)} \frac{h}{2\pi} = \sqrt{0} = 0 \]
Thus, the orbital angular momentum for an s-electron is indeed zero.

### Conclusion
- The first statement is incorrect.
- The second statement is correct.

The correct option is **B** (only the second statement is correct).