Question

In the sixth period, the orbitals which are completely filled are (a) \(6 \mathrm{~s}, 6 \mathrm{p}, 5 \mathrm{~d}, 5 \mathrm{f}\) (b) \(6 s, 6 p, 6 d, 6 f\) (c) \(6 \mathrm{~s}, 5 \mathrm{f}, 6 \mathrm{~d}, 6 \mathrm{p}\) (d) \(6 s, 4 f, 5 d, 6 p\)

Short answer

Answer: (d) 6s, 4f, 5d, 6p

Step-by-step solution

Recall the order of filling electron configuration

According to the aufbau principle, the order of filling is 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d and so on.

Identify elements in the sixth period

The sixth period of the periodic table includes elements with atomic numbers ranging from 55 (Cs) to 86 (Rn). We need to find which orbitals are completely filled during this period.

Determine completely filled orbitals

Following the order of filling electron configuration, we can observe that the last filled orbital before the sixth period is 5p, and the first filled orbital in the next period (seventh) is 7s. So the completely filled orbitals in the sixth period are: \(6s, 4f, 5d,\) and \(6p\)

Compare the options with the actual configuration

Comparing the options given in the exercise with the actual configuration we found: (a) \(6 \mathrm{~s}, 6 \mathrm{p}, 5 \mathrm{~d}, 5 \mathrm{f}\) (b) \(6 s, 6 p, 6 d, 6 f\) (c) \(6 \mathrm{~s}, 5 \mathrm{f}, 6 \mathrm{~d}, 6 \mathrm{p}\) (d) \(6 s, 4 f, 5 d, 6 p\) Only option (d) matches the actual configuration, so that is the correct answer.

Key concepts

Electron Filling Order

Understanding the electron filling order is key to determining how electrons populate orbitals as elements increase in atomic number. Electrons are filled into atomic orbitals according to an increasing energy order. This method allows for the most stable electronic arrangement possible. The sequence for filling electrons is based on both energy and order of orbitals:

• Starts with the lowest energy level, beginning with the 1s orbital, then 2s, and so on.
• The electron configuration progresses through various s, p, d, and f orbitals.
• The order isn't straightforward past the third energy level where 4s is filled before 3d.

Memorizing this electron filling order can be facilitated with the use of a chart or diagram, which illustrates the sequence in which orbitals are filled. You’ll often progress through orbitals like this: 1s, 2s, 2p, 3s, 3p, 4s, 3d, and continue using the Aufbau principle, which we'll discuss next.

Aufbau Principle

The Aufbau principle is crucial for understanding how orbitals are populated with electrons. The term 'Aufbau' is German for "building up" or "construction," reflecting how electrons accumulate configuration in an atom.

• Electrons enter orbitals starting from the lowest energy level to the highest.
• It utilizes the principle that orbitals within a given energy level aren't always filled before orbitals of a higher energy level, e.g., the 4s is filled before the 3d.
• Exceptions to the Aufbau principle exist for some transition metals and heavier elements due to energy shifts in orbitals.

The Aufbau principle also involves Hund’s Rule and the Pauli Exclusion Principle, which govern that an electron will fill each subshell singly before pairing, and no two electrons can have the same set of quantum numbers.

Periodic Table Sixth Period

The sixth period of the periodic table is unique due to its variety of elements and filled orbitals. This period begins with Cesium (Cs), atomic number 55, and ends with Radon (Rn), atomic number 86.

• This section includes lanthanides, where the 4f orbitals are filled.
• The sequence of filled orbitals in this period is: 6s, 4f, 5d, and finally, 6p.
• Nodes and nuances in filling arise due to the transition from 4f to 5d orbitals, making understanding the order of electron filling particularly essential here.

Each element within this sixth period follows a specific electron configuration pattern based on their position in the periodic table, emphasizing the systematic nature of electron arrangements as you move through these elements.

Completely Filled Orbitals

In considering which orbitals are completely filled, especially in different periods, it's about recognizing final options through filled electron configurations. An orbital is completely filled when it holds the maximum number of electrons possible.

• s orbitals can hold up to 2 electrons.
• p orbitals can accommodate 6 electrons.
• d orbitals are filled with 10 electrons.
• f orbitals have a maximum capacity of 14 electrons.

In the sixth period, as calculated with our electron filling order, the completely filled orbitals found in the configurations are: 6s, 4f, 5d, and 6p. This information is essential to correctly deduce the answers to such configurations and align with empirical observations such as atomic spectra and periodic trends.