Question

How many orbitals would you expect to find in the last subshell of the fifth shell? How many electrons would you need to fill this subshell?

Short answer

9 orbitals in 5g subshell; 18 electrons needed.

Step-by-step solution

Understanding Electron Shells

The fifth shell (also known as the 5th electron shell) is defined by the principal quantum number, n = 5. This indicates the number of subshells contained within this shell.

Identifying the Subshells in the Fifth Shell

The fifth shell (n = 5) contains 5 subshells: 5s, 5p, 5d, 5f, and 5g. Each subshell is characterized by a specific set of orbitals: s (1 orbital), p (3 orbitals), d (5 orbitals), f (7 orbitals), and g (9 orbitals).

Finding the Last Subshell

In this progression, the last subshell in the fifth shell is 5g, as it builds sequentially after 5f.

Counting the Orbitals in the 5g Subshell

The 'g' subshell contains 9 orbitals. This is confirmed through the pattern where the azimuthal quantum number, l, determines the number of orbitals by the formula: number of orbitals = 2l + 1. For g, l=4, leading to 9 orbitals.

Calculating the Electrons Needed to Fill 5g Subshell

Each orbital can hold 2 electrons. Therefore, to fill all 9 orbitals in the 5g subshell, you would need 9 x 2 = 18 electrons.

Key concepts

Quantum Numbers

Quantum numbers are essential for understanding the arrangement of electrons within an atom. They are like the address system for electrons, determining an electron's position within an atom. There are four main quantum numbers:

• Principal Quantum Number (n): Represents the main energy level or shell an electron occupies. It is a positive integer (n = 1, 2, 3...). Higher values mean the electron is located further from the nucleus.


• Azimuthal Quantum Number (l): Indicates the subshell type within a shell and is related to the shape of the orbital. It is an integer ranging from 0 to (n-1). For instance, in the n=5 shell, l can be 0 (s), 1 (p), 2 (d), 3 (f), and 4 (g).


• Magnetic Quantum Number (m_l): Describes the specific orbital within a subshell where an electron is likely to be found. It can take on values between -l and +l.


• Spin Quantum Number (m_s): Indicates the direction of the electron's spin, which can be either +1/2 or -1/2.

Understanding these numbers helps us determine the distribution of electrons in atoms, which in turn explains chemical properties and behaviors.

Electron Shells

Electron shells are like layers around the nucleus of an atom, housing the electrons. Each shell corresponds to a principal quantum number, denoted as 'n'. The higher the number 'n', the further the shell is from the nucleus, and it can accommodate more electrons.

• The first shell (n=1) is the closest to the nucleus and has the least energy. As 'n' increases, so does the energy level of the shell.


• Each shell can hold a maximum of 2n² electrons. For example, the 1st shell can hold up to 2 electrons, the 2nd shell up to 8, and so on.


• Electrons fill from the lowest energy level to the highest, following the Aufbau principle, which explains the electron configuration in atoms.

Understanding electron shells helps us conceive how electrons are structured in atoms and predict their chemical properties.

Subshells

Subshells are contained within the larger electron shells and define the shape and energy of the orbitals in that region. Each subshell corresponds to a different azimuthal quantum number 'l'.

• The s subshell (l=0) is spherical and contains one orbital.


• The p subshell (l=1) has a dumbbell shape and consists of three orbitals.


• The d subshell (l=2) has a more complex shape and five orbitals.


• The f subshell (l=3) is even more complex with seven orbitals.


• At the fifth shell, we also encounter the g subshell (l=4), which comprises nine orbitals.

The number of orbitals in each subshell can be determined by the formula: 2l + 1. More orbitals allow for a greater number of electrons. Subshell shapes influence how atoms bond and interact with each other.

Orbitals

Orbitals are regions within a subshell where electrons are most likely to be found. Each orbital can hold up to two electrons, with opposite spins.

• Orbital Shapes: The shape of an orbital depends on its subshell type. For example, s orbitals are spherical, while p orbitals are dumbbell-shaped.


• Orbitals in Subshells: Each type of subshell has a specific number of orbitals. S subshells have 1, p has 3, d has 5, f has 7, and g subshells have 9 orbitals. The equation 2l + 1 helps calculate these numbers.


• Electron Capacity: They can hold two electrons each, leading to different capacities across subshells. For instance, the g subshell with its 9 orbitals can accommodate 18 electrons in total.

Understanding orbitals helps predict an atom's behavior and its interactions in chemical reactions, as the location and arrangement of electrons are crucial for these processes.