How many electrons with l=2 are there in an atom having atomic number 21 ?

Options

A. 3
B. 4
C. 10
D. 1

Explanation

To determine how many electrons with l=2 are present in an atom with atomic number 21, we can follow these steps:

### Step 1: Understand the Quantum Numbers
The azimuthal quantum number (l) indicates the shape of the orbital. For l=2, the corresponding orbital is the d orbital.

### Step 2: Identify the Atomic Number
The atomic number (Z) of the atom is given as 21. This means the atom has 21 electrons.

### Step 3: Write the Electronic Configuration
To find the distribution of these electrons, we need to write the electronic configuration of the atom with atomic number 21. The electronic configuration is filled according to the Aufbau principle, Hund's rule, and the Pauli exclusion principle.

1. The first two electrons fill the 1s orbital: **1s²**
2. The next two electrons fill the 2s orbital: **2s²**
3. The next six electrons fill the 2p orbital: **2p⁶**
4. The next two electrons fill the 3s orbital: **3s²**
5. The next six electrons fill the 3p orbital: **3p⁶**
6. The remaining three electrons will fill the 4s and 3d orbitals. The 4s orbital is filled before the 3d orbital: **4s² 3d¹**

Thus, the complete electronic configuration for the atom with atomic number 21 (Scandium) is:
\[ \text{1s}^2 \, \text{2s}^2 \, \text{2p}^6 \, \text{3s}^2 \, \text{3p}^6 \, \text{4s}^2 \, \text{3d}^1 \]

### Step 4: Count the Electrons in the d Orbital
From the electronic configuration, we can see that there is **1 electron** in the 3d orbital (which corresponds to l=2).

### Conclusion
Therefore, the number of electrons with l=2 in an atom with atomic number 21 is **1**.

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