Question

Determine the identity of the element that contains exactly (a) three \(4 p\) electrons in the ground state (b) seven \(3 d\) electrons in the ground state (c) one \(2 s\) electrons in the ground state (d) five \(3 p\) electrons in the ground state

Short answer

The respective elements are (a) arsenic (As), (b) cobalt (Co), (c) lithium (Li), and (d) chlorine (Cl).

Step-by-step solution

Determine the element with three 4p electrons in the ground state

To find the element with three 4p electrons in the ground state, first fill the electron shells in order up to the 4p orbital following Hund's rule and the aufbau principle. The 4p orbital begins filling after the 3d orbital. After the 3d orbital is filled with 10 electrons, the 4s orbital is filled with 2 electrons, making a total of 12 electrons after the 3d shell. The element that has exactly three 4p electrons is the one which has three more electrons after the 3d10 4s2 configuration, which is arsenic (As) with an atomic number of 33.

Determine the element with seven 3d electrons in the ground state

Identifying the element with seven 3d electrons is accomplished by filling the electron configurations up to the 3d subshell. The 3d orbital begins to fill after the 4s orbital according to the aufbau principle. After 4s is filled with 2 electrons, seven 3d electrons would mean that the element is in the transition metals category. Cobalt (Co) with an atomic number of 27 has an electron configuration of [Ar] 4s2 3d7, which means it has seven 3d electrons.

Determine the element with one 2s electron in the ground state

The element that contains one 2s electron in the ground state is found by filling up the 1s subshell with 2 electrons first and then adding one electron to the 2s subshell. Hydrogen and helium both fill up the 1s subshell. The next element, lithium (Li) with an atomic number of 3, has the electron configuration [He] 2s1, meaning it has one 2s electron.

Determine the element with five 3p electrons in the ground state

To determine the element with five 3p electrons in the ground state, electron configurations must be filled up to the 3p subshell. After the 3s subshell is filled with 2 electrons, adding 5 electrons to the 3p subshell gives us the electron configuration of the element. Phosphorus (P) with an atomic number of 15 has an electron configuration of [Ne] 3s2 3p3. Therefore, it does not match the condition. However, adding two more electrons in the p subshell, chlorine (Cl) with an atomic number of 17 has the electron configuration [Ne] 3s2 3p5. Hence, chlorine is the element with exactly five 3p electrons.

Key concepts

Ground State Electron Configuration

Understanding the ground state electron configuration is essential for knowing how electrons are distributed in an atom in its most stable form. The ground state refers to the lowest energy state of an atom, where all its electrons are in the lowest possible energy levels or orbitals. When solving problems like determining the identity of elements based on their electron configuration, it's crucial to consider the ground state.

For instance, identifying an element with three 4p electrons implies that all other orbitals lower in energy are filled according to the electron configuration rules. The ground state is significant because any excitation to a higher state would require energy input, and the atom would not be in its most stable configuration. Elements in their ground state, therefore, follow a specific order of filling orbitals known as the aufbau principle, obey the maximum capacity of electrons in each sublevel, and align with Hund's rule for orbital filling.

Aufbau Principle

The aufbau principle is like a map that guides the filling order of electron orbitals. This principle states that electrons fill orbitals starting at the lowest energy level and move to higher levels progressively. The sequence is determined by the sum of the principal quantum number (n) and the azimuthal quantum number (l). Orbitals with a lower sum of n + l get filled first.

• 1s is filled before 2s (since 1 + 0 < 2 + 0)
• 2p is filled after 2s but before 3s (since 2 + 1 < 3 + 0)
• Following the filling order, after 3d comes 4s because 3p is filled before (although 4s is energetically lower than 3d).

These rules are crucial for correctly identifying element (a) arsenic with three 4p electrons, since we know that orbitals up to 3d and 4s should be filled first. The aufbau principle, paired with Hund's rule, gives us a predictive tool for determining the electronic configurations of elements in their ground states.

Hund's Rule

Moving on to Hund's Rule, this rule addresses the way electrons distribute themselves among orbitals of the same sublevel. According to Hund's rule, electrons will fill an empty orbital before they pair up in an already occupied one. This minimizes electron repulsion and maximizes the total spin, leading to greater stability of the atom.

When looking at the example of chlorine, which requires five 3p electrons, Hund's rule explains why these electrons occupy three different p orbitals with parallel spins before any pairing occurs. Similarly, in pairing electrons, each electron in a pair must have opposite spin to align with the Pauli exclusion principle, which states that no two electrons in the same atom can have identical quantum numbers.

Considering Hund's rule ensures that we correctly determine the electron configurations, especially when we deal with partially filled orbitals as in the case of cobalt, which has seven 3d electrons spread out in five orbitals following this principle.