Question

The periodic table consists of four blocks of elements that cor- respond to \(s, p, d,\) and \(f\) orbitals being filled. After \(f\) orbitals come \(g\) and \(h\) orbitals. In theory, if a \(g\) block and an \(h\) block of elements existed, how long would the rows of \(g\) and \(h\) elements be in this theoretical periodic table?

Short answer

In a theoretical periodic table with 'g' and 'h' orbitals, the 'g' block rows would consist of 18 elements, while the 'h' block rows would consist of 22 elements. This is determined by calculating the maximum number of electrons that can be held by the respective orbitals using the formula \( 2(2l + 1) \), where l is the azimuthal quantum number.

Step-by-step solution

Determine the 'g' block element rows length

To find the length of the 'g' block element rows, we need to calculate the number of electrons that can be held by the 'g' orbitals. The 'g' orbitals follow the 'f' orbitals in the order, so they will hold more electrons than the 'f' orbitals. The general rule is that the maximum number of electrons that can be accommodated in a set of orbitals with a given azimuthal quantum number l is given by: \( 2(2l + 1) \) For 'g' orbitals, the azimuthal quantum number l is 4 (s - 0, p - 1, d - 2, f - 3, g - 4). Now let's apply the formula to find the maximum electrons that can be held by 'g' orbitals: \( 2(2(4) + 1) = 2(9) = 18 \) The 'g' block would consist of 18 elements in a row.

Determine the 'h' block element rows length

Similarly, we can determine the number of elements in the 'h' block element rows by calculating the number of electrons that can be held by the 'h' orbitals. The 'h' orbitals follow the 'g' orbitals in the order, so they will hold more electrons than the 'g' orbitals. For 'h' orbitals, the azimuthal quantum number l is 5 (s - 0, p - 1, d - 2, f - 3, g - 4, h - 5). Now let's apply the formula to find the maximum electrons that can be held by 'h' orbitals: \( 2(2(5) + 1) = 2(11) = 22 \) The 'h' block would consist of 22 elements in a row. In conclusion, in this theoretical periodic table, the 'g' block rows would be 18 elements long, and the 'h' block rows would be 22 elements long.

Key concepts

Atomic Orbitals

Atomic orbitals are regions in space around the nucleus where electrons are most likely to be found. Each orbital has a specific shape and energy level that corresponds to the electron's quantum state. The primary types of atomic orbitals include:

• s orbitals: Spherical in shape and can hold up to two electrons.
• p orbitals: Dumbbell-shaped and can hold up to six electrons across three sub-orbitals.
• d orbitals: Have more complex shapes and can hold up to ten electrons across five sub-orbitals.
• f orbitals: Even more complex and can hold up to fourteen electrons across seven sub-orbitals.

When considering additional theoretical orbitals such as g or h, the complexity increases further. The shape of these orbitals would expand geometrically and include more nodal planes, which affect where electrons are likely to be found. Generally, the higher the energy orbital, the further it extends from the nucleus, offering electrons a greater range of space within which they can move.

Electron Configuration

Electron configuration is the arrangement of electrons within an atom. The configuration describes how electrons populate various atomic orbitals according to certain rules. These rules include the Pauli exclusion principle, Hund's rule, and the Aufbau principle.

• Pauli Exclusion Principle: States that no two electrons can have the same set of quantum numbers; hence, an orbital can hold a maximum of two electrons with opposite spins.
• Hund's Rule: Electrons will fill an unoccupied orbital before they pair up in an already occupied one to minimize repulsion.
• Aufbau Principle: Electrons initially occupy the lowest energy orbitals available before filling higher energy levels.

Using these principles, electronic configuration helps determine the chemical properties of an element. For instance, the filling of orbitals (like s, p, d, and f orbitals) characterizes different blocks of the periodic table. With the introduction of theoretical blocks such as g and h, the electron configuration would extend to encompass higher energy levels and more complex atomic structures, accommodating more electrons along the way.

Quantum Numbers

Quantum numbers describe the specific configuration of electrons in an atom, essentially providing a "GPS" for where each electron can be found. There are four major quantum numbers, each offering unique information:

• Principal Quantum Number (\( n \)): Indicates the electron's energy level or shell. The higher the value of \( n \), the larger and more energetic the orbitals.
• Azimuthal Quantum Number (\( l \)): Defines the shape of the orbital. The values range from 0 up to \( n-1 \). For example, \( l = 0 \) indicates an \( s \) orbital, \( l = 1 \) a \( p \) orbital, and so on.
• Magnetic Quantum Number (\( m_l \)): Describes the orientation of the orbital in space with values ranging from \( -l \) to \( +l \).
• Spin Quantum Number (\( m_s \)): Represents the electron's spin direction, having two possible values: \( +\frac{1}{2} \) or \( -\frac{1}{2} \).

These quantum numbers not only help describe existing elements within the periodic table but are crucial for conceptualizing and predicting the properties of potential new elements, such as those theorized within the \( g \) and \( h \) blocks. These would simply continue the pattern established by known orbitals, using their sequentially higher azimuthal values.