Question

Which electronic configuration does not follow Pauli's exclusion principle? (1) \(1 \mathrm{~s}^{2} 2 \mathrm{~s}^{2} 2 \mathrm{p}^{4}\) (2) \(1 \mathrm{~s}^{2} 2 \mathrm{~s}^{2} 2 \mathrm{p}^{4} 4 \mathrm{~s}^{2}\) (3) \(1 s^{2} 2 p^{4}\) (4) \(1 \mathrm{~s}^{2} 2 \mathrm{~s}^{2} 2 \mathrm{p}^{6} 3 \mathrm{~s}^{3}\)

Short answer

Configuration (4) \(1 \,\mathrm{~s}^{2} \, 2 \,\mathrm{~s}^{2} \, 2 \,\mathrm{p}^{6} \, 3 \,\mathrm{~s}^{3}\) does not follow Pauli's exclusion principle.

Step-by-step solution

- Understand Pauli's Exclusion Principle

Pauli's Exclusion Principle states that no two electrons in an atom can have the same set of four quantum numbers. This means each orbital can hold a maximum of two electrons with opposite spins.

- Examine Configuration (1)

Configuration (1) is \(1 \,\mathrm{~s}^{2} \, 2 \,\mathrm{~s}^{2} \, 2 \,\mathrm{p}^{4}\). Each of these subshells does not exceed the maximum electron count allowed by Pauli's exclusion principle. Thus, it follows the principle.

- Examine Configuration (2)

Configuration (2) is \(1 \,\mathrm{~s}^{2} \, 2 \,\mathrm{~s}^{2} \, 2 \,\mathrm{p}^{4} \, 4 \,\mathrm{~s}^{2}\). Each of these subshells also does not exceed the maximum electron count. Thus, it follows the principle.

- Examine Configuration (3)

Configuration (3) is \(1 \,\mathrm{s}^{2} \, 2 \,\mathrm{p}^{4}\). However, there is no 2s subshell listed. This configuration skips a subshell, but it does not violate Pauli's Exclusion principle directly since it still respects the maximum limits per subshell.

- Examine Configuration (4)

Configuration (4) is \(1 \,\mathrm{~s}^{2} \, 2 \,\mathrm{~s}^{2} \, 2 \,\mathrm{p}^{6} \, 3 \,\mathrm{~s}^{3}\). Here, the 3s subshell has three electrons, which exceeds the permissible two electrons per orbital limit, hence violating Pauli's Exclusion Principle.

Key concepts

Electronic Configuration

Electronic configuration describes the arrangement of electrons in an atom. This arrangement follows a specific order based on the increasing energy levels of the orbitals. For example, in the case of an oxygen atom with the atomic number 8, its electron configuration will be \[1s^{2} \ 2s^{2} \ 2p^{4} \]. This shows that the 1s subshell is filled first, followed by the 2s subshell, and then the 2p subshell. Each subshell is filled according to its capacity, in a manner that minimizes the atom's energy.
It is important to follow certain rules and principles to correctly write an electronic configuration:

• Aufbau Principle: Electrons fill orbitals starting from the lowest energy level to the highest.
• Pauli's Exclusion Principle: No two electrons in an atom can have the same set of four quantum numbers.
• Hund's Rule: Each orbital in a subshell gets one electron before any orbital gets a second electron.

Quantum Numbers

Quantum numbers are crucial for understanding the properties and behavior of electrons within an atom. They describe the position and energy of an electron:

• Principal Quantum Number (n): Indicates the energy level and size of the orbital (e.g., n=1, 2, 3,...).
• Angular Momentum Quantum Number (l): Determines the shape of the orbital and ranges from 0 to n-1 (e.g., l=0 for s, l=1 for p, l=2 for d, and so on).
• Magnetic Quantum Number (m_l): Specifies the orientation of the orbital in space and ranges from -l to +l.
• Spin Quantum Number (m_s): Indicates the spin of the electron and can be either +1/2 or -1/2.

According to Pauli’s Exclusion Principle, no two electrons in the same atom can have the same four quantum numbers, ensuring that each electron's position and energy is unique within an atom.

Subshell Limits

Subshells are subdivisions of electron shells, within which orbitals group together. Each type of subshell has a specific limit to the number of electrons it can hold:

• s-subshell: Can hold a maximum of 2 electrons.
• p-subshell: Can accommodate up to 6 electrons.
• d-subshell: Can hold up to 10 electrons.
• f-subshell: Can accommodate 14 electrons.

Pauli’s Exclusion Principle specifically dictates that an orbital within these subshells can hold a maximum of 2 electrons with opposite spins. This is why configuration (4) in the exercise is incorrect. The 3s subshell has three electrons, surpassing the limit of 2, thus violating the principle. Understanding these limits is essential for accurately writing and interpreting electronic configurations.