considering the electron of outermost orbital of CU match the items given the column I with their values given in column II. Column-I { (A) orbital angular momentum, (B) angular momentum in an orbit, (C) spin angular momentum} Column - II ( I. 4h, II. 0, III. 0.86h, IV. 1.73)

Options

A. A(II),B(I), C(III)
B. A(III),B(IV),C(II)
C. A(I),B(IV),C(II)
D. A(I),B(II),C(III)

Answer

To solve the problem of matching the items in Column I with their corresponding values in Column II for the outermost electron of copper (Cu), we will follow these steps:

### Step 1: Determine the electronic configuration of copper
Copper (Cu) has an atomic number of 29. The electronic configuration is:
- 1s² 2s² 2p⁶ 3s² 3p⁶ 3d¹⁰ 4s¹

The outermost electrons are in the 4s and 3d orbitals.

### Step 2: Identify the outermost orbital
The outermost orbital for the electron in copper is the 4s orbital, which contains one electron.

### Step 3: Calculate the orbital angular momentum (L)
The formula for orbital angular momentum is given by:
\[ L = l \cdot \hbar \]
where \( l \) is the azimuthal quantum number. For the s orbital, \( l = 0 \).

However, since we are considering the outermost orbital (4s), we need to calculate the total orbital angular momentum for the outermost electron:
- For the 4s orbital, \( l = 0 \)
- Therefore, the orbital angular momentum \( L = 0 \cdot \hbar = 0 \)

### Step 4: Calculate the total angular momentum in an orbit
The total angular momentum in an orbit is also determined by the quantum number \( l \). Since the outermost electron is in the s orbital:
- \( L = 0 \)

### Step 5: Calculate the spin angular momentum (S)
The formula for spin angular momentum is:
\[ S = \sqrt{s(s + 1)} \cdot \hbar \]
where \( s \) is the spin quantum number. For an electron, \( s = \frac{1}{2} \).

Calculating the spin angular momentum:
\[ S = \sqrt{\frac{1}{2} \left(\frac{1}{2} + 1\right)} \cdot \hbar = \sqrt{\frac{1}{2} \cdot \frac{3}{2}} \cdot \hbar = \sqrt{\frac{3}{4}} \cdot \hbar = \frac{\sqrt{3}}{2} \cdot \hbar \]

Using the approximate value of \( \sqrt{3} \approx 1.73 \):
\[ S \approx 0.86 \hbar \]

### Step 6: Match the values from Column I to Column II
Now we can match the calculated values with those in Column II:
- (A) Orbital angular momentum: \( 0 \) (matches with II)
- (B) Angular momentum in an orbit: \( 0 \) (matches with II)
- (C) Spin angular momentum: \( 0.86 \hbar \) (matches with III)

### Final Matching
- A matches with II (0)
- B matches with I (4h)
- C matches with III (0.86h)

Thus, the final matches are:
- A → II
- B → I
- C → III