On the basis of quantum numbers, justify that the fourth period of the Modern periodic table should have `18` elements.

Answer

To justify that the fourth period of the Modern periodic table should have 18 elements based on quantum numbers, we can follow these steps:

### Step 1: Understand Quantum Numbers and Electron Configuration
Quantum numbers describe the properties of atomic orbitals and the electrons in those orbitals. The four quantum numbers are:
1. Principal quantum number (n) - indicates the energy level.
2. Azimuthal quantum number (l) - indicates the shape of the orbital.
3. Magnetic quantum number (m_l) - indicates the orientation of the orbital.
4. Spin quantum number (m_s) - indicates the spin of the electron.

### Step 2: Identify the Fourth Period
The fourth period corresponds to the principal quantum number n = 4. In this period, we will fill the following orbitals:
- 4s
- 3d
- 4p

### Step 3: Fill the Orbitals According to the Aufbau Principle
According to the Aufbau principle, electrons fill orbitals starting from the lowest energy level to the highest. The order of filling for the fourth period is:
1. 4s
2. 3d
3. 4p

### Step 4: Count the Maximum Number of Electrons in Each Subshell
- **4s subshell**: Can hold a maximum of 2 electrons (4s²).
- **3d subshell**: Can hold a maximum of 10 electrons (3d¹⁰).
- **4p subshell**: Can hold a maximum of 6 electrons (4p⁶).

### Step 5: Calculate the Total Number of Electrons
Now, we can sum the maximum number of electrons that can be accommodated in the fourth period:
- Electrons in 4s = 2
- Electrons in 3d = 10
- Electrons in 4p = 6

Total = 2 (from 4s) + 10 (from 3d) + 6 (from 4p) = 18 electrons.

### Conclusion
Thus, the fourth period of the Modern periodic table can accommodate a maximum of 18 elements based on the filling of the 4s, 3d, and 4p orbitals.

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