Question

Which of the following electron configurations are for atoms in the ground state? In the excited state? Which are impossible? (a) \(1 s^{2} 2 s^{2} 2 p^{1}\) (b) \(1 s^{2} 1 p^{1} 2 s^{1}\) (c) \(1 s^{2} 2 s^{2} 2 p^{3} 3 s^{1}\) (d) \(1 s^{2} 2 s^{2} 2 p^{6} 3 d^{10}\) (e) \(1 s^{2} 2 s^{2} 2 p^{5} 3 s^{1}\)

Short answer

Question: Determine whether each electron configuration represents the ground state, excited state, or is impossible. (a) \(1 s^{2} 2 s^{2} 2 p^{1}\) (b) \(1 s^{2} 1 p^{1} 2 s^{1}\) (c) \(1 s^{2} 2 s^{2} 2 p^{3} 3 s^{1}\) (d) \(1 s^{2} 2 s^{2} 2 p^{6} 3 d^{10}\) (e) \(1 s^{2} 2 s^{2} 2 p^{5} 3 s^{1}\) Answer: - Ground state: (a) and (e) - Excited state: (c) - Impossible: (b) and (d)

Step-by-step solution

Verify the Pauli Exclusion Principle

The Pauli Exclusion Principle states that no two electrons can have the same four quantum numbers. This means that each orbital (s, p, d, f) can have a maximum of 2 electrons and their spins must be opposite. Check the given configurations and make sure that no orbital has more than 2 electrons.

Verify the Aufbau Principle

The Aufbau Principle states that electrons must occupy the lowest energy levels before moving to higher energy levels. This means that electron configurations should follow the order of the Aufbau diagram: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, etc. Check each configuration and make sure it follows this order.

Verify Hund's Rule

Hund's Rule states that orbitals of equal energy should be occupied by one electron each before doubling up. This means that p, d, and f orbitals must be completely occupied by single electrons before any double occupancy happens. Check each configuration and make sure it follows Hund's Rule. Now, let's apply these steps to each configuration:

Configuration (a)

(a) \(1 s^{2} 2 s^{2} 2 p^{1}\) This configuration follows all three rules mentioned above. As it fills up the orbitals in order, it represents an atom in the ground state.

Configuration (b)

(b) \(1 s^{2} 1 p^{1} 2 s^{1}\) This configuration violates the Aufbau Principle, as there are no 1p orbitals. This configuration is impossible.

Configuration (c)

(c) \(1 s^{2} 2 s^{2} 2 p^{3} 3 s^{1}\) This configuration violates the Aufbau Principle, as the 3s orbital should be fully occupied before moving on to the 3p orbitals. This configuration represents an atom in an excited state

Configuration (d)

(d) \(1 s^{2} 2 s^{2} 2 p^{6} 3 d^{10}\) This configuration follows all three rules mentioned above but violates the Aufbau Principle, as the 3d orbitals should be filled after the 4s and 3p orbitals. This configuration is impossible.

Configuration (e)

(e) \(1 s^{2} 2 s^{2} 2 p^{5} 3 s^{1}\) This configuration follows all three rules mentioned above. As it fills up the orbitals in order, it represents an atom in the ground state. In conclusion: - Ground state: (a) and (e) - Excited state: (c) - Impossible: (b) and (d)

Key concepts

Pauli Exclusion Principle

When learning about electron configurations, one of the fundamental rules to grasp is the Pauli Exclusion Principle. This principle, proposed by Wolfgang Pauli in 1925, provides a crucial insight into the behavior of electrons within an atom.

The Pauli Exclusion Principle states that no two electrons in an atom can have the same set of four quantum numbers. Remember that each electron's state in an atom can be identified by a unique set of these numbers, which denote its energy level (principal quantum number), shape of the orbital (angular quantum number), orientation of the orbital (magnetic quantum number), and spin direction (spin quantum number).

In practice, this means that an atomic orbital – be it s, p, d, or f – can hold a maximum of two electrons, and they must have opposing spins. This is visually represented by one arrow pointing up and the other down when filling orbitals in electron configuration diagrams.

The principle enforces an orderly filling of electrons in an atom and ensures that electron configurations are built by adding electrons successively to avoid replication of quantum states. This is foundational for understanding why certain electron configurations are possible while others, like configuration (b) \(1 s^{2} 1 p^{1} 2 s^{1}\), are not.

Aufbau Principle

The Aufbau Principle helps us determine the sequence in which orbitals are filled as electrons are added to an atom. Aufbau is German for 'building up,' and the principle guides us in building up the electronic structure of an atom from the ground up.

Electrons fill the lowest energy orbitals first. This begins with the 1s orbital, which is the closest to the nucleus and therefore has the lowest energy. From there, electrons are placed in the 2s, then the 2p, and proceeding in a specific order: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, and so on. This hierarchy follows the (n+l) rule, where 'n' is the principal quantum number and 'l' is the azimuthal quantum number.

Configuration (d) \(1 s^{2} 2 s^{2} 2 p^{6} 3 d^{10}\) showcases a violation of the Aufbau Principle because electrons are incorrectly assigned to the 3d orbitals before filling the 4s orbital. Without adherence to this principle, the predicted chemical and physical properties of atoms would be significantly skewed.

Hund's Rule

Another essential concept to understand when predicting electron configurations is Hund's Rule. This rule focuses on the distribution of electrons across orbitals of the same energy, known as 'degenerate orbitals'.

Hund's Rule states that electrons must be placed into separate orbitals of the same energy level before they are paired up in an orbital. When occupying these orbitals, the electrons will have the same spin. This principle minimizes electron repulsion within the atom and ultimately stabilizes the electron configuration.

Example of Hund's Rule

Consider configuration (a) \(1 s^{2} 2 s^{2} 2 p^{1}\). Here, the single 2p electron is correctly placed in an empty 2p orbital, following Hund's Rule. If another electron were to be added to the 2p sublevel, it would occupy one of the other two empty 2p orbitals, not pair up with the first 2p electron, keeping with the rule's requirement. Failure to apply Hund's Rule correctly can lead to incorrect predictions about the atom's behavior, particularly in regard to its magnetic properties and chemical reactivity.