Which one is wrong statement?

Options

A. Total orbital angular momentum of electron in 's' orbital is equal to zero
B. An orbital is designated by three quantum numbers while an electron in an atom is designated by four quntum numbers
C. The electronic configuration of N atoms is
D. The value of m for `d_(Z)^2` is zero

Answer

To determine which statement is incorrect, we will evaluate each statement one by one.

### Step 1: Evaluate Statement A
**Statement A:** "Total orbital angular momentum of electron in s orbital is equal to zero."

- **Explanation:** The orbital angular momentum (L) is calculated using the formula:
\[ L = \sqrt{l(l + 1)} \cdot \frac{h}{2\pi} \]
For an s orbital, the azimuthal quantum number \( l = 0 \). Therefore, substituting \( l = 0 \):
\[ L = \sqrt{0(0 + 1)} \cdot \frac{h}{2\pi} = 0 \]
Thus, this statement is **correct**.

### Step 2: Evaluate Statement B
**Statement B:** "An orbital is designated by three quantum numbers while the electron in an atom is designated by the four quantum numbers."

- **Explanation:** To designate an orbital, we need three quantum numbers: the principal quantum number (n), the azimuthal quantum number (l), and the magnetic quantum number (m). To designate an electron, we need four quantum numbers: n, l, m, and the spin quantum number (s). Therefore, this statement is also **correct**.

### Step 3: Evaluate Statement C
**Statement C:** "The electronic configuration of nitrogen atom is incorrect."

- **Explanation:** The correct electronic configuration of nitrogen (atomic number 7) is \( 1s^2 2s^2 2p^3 \). According to Hund's rule, electrons in the same subshell (like 2p) must occupy empty orbitals singly before pairing up to maximize total spin. If the configuration violates this rule, it is incorrect. If the statement claims an incorrect configuration, then this statement is **incorrect**.

### Step 4: Evaluate Statement D
**Statement D:** "The value of m for \( d_z \) is equal to 0."

- **Explanation:** The magnetic quantum number \( m \) can take values from \(-l\) to \(+l\). For d orbitals, \( l = 2 \), so \( m \) can be -2, -1, 0, 1, or 2. The \( d_z \) orbital corresponds to \( m = 0 \). Thus, this statement is **correct**.

### Conclusion
The incorrect statement is **Statement C**, which claims an incorrect electronic configuration for nitrogen.

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