Four electrons in an atom have the sets of quantum numbers as given below. Which electron in at the highest energy level? (a) \(n=4, l=0, m_{l}=0, m_{s}=+1 / 2\) (b) \(n=3, l=0, m_{l}=0, m_{s}=-1 / 2\) (c) \(n=3, l=2, m_{l}=0, m_{s}=+1 / 2\) (d) \(n=4, l=1, m_{l}=-1, m_{s}=-1 / 2\)

The principal quantum number, denoted by the symbol 'n', plays a crucial role in determining the energy level and size of an atomic orbital where an electron resides. It is an integer starting from 1 and increases with the energy level of the electron in the atom.

As 'n' increases, the electron's orbital becomes larger and the electron is further from the nucleus, which means it has a higher energy level. For example, an electron in the first energy level would have a principal quantum number of 1, while an electron in the second energy level would have a principal quantum number of 2, and so on. Moreover, the difference in energy between these levels decreases as 'n' gets larger.

In the context of the given exercise, among the options provided, the higher the value of 'n', the higher the energy level of the electron. This concept is crucial for understanding the arrangement of electrons in atoms and their subsequent chemical behavior.

The azimuthal quantum number, often represented by 'l', defines the shape of an atomic orbital and is sometimes referred to as the angular momentum quantum number. It can take on any integer value from 0 to 'n-1', where 'n' is the principal quantum number.

Each value of 'l' corresponds to a specific type of orbital: 0 for s orbitals, 1 for p orbitals, 2 for d orbitals, and 3 for f orbitals. The value of 'l' not only influences the shape but also determines the number of orbitals in a given subshell: there is 1 s orbital, 3 p orbitals, 5 d orbitals, and 7 f orbitals.

Applying this to the provided exercise, when energy levels are being compared, an electron with a higher azimuthal quantum number will be at a higher energy level if the principal quantum numbers are the same. Therefore, an electron in a p orbital (l = 1) is at a higher energy level than an electron in an s orbital (l = 0) within the same principal energy level.

Atomic orbitals are the regions of space around an atom's nucleus where there is a high probability of finding an electron. They are defined by the quantum numbers and are crucial for understanding electron distribution within an atom.

The shape and size of these orbitals are determined primarily by the principal and azimuthal quantum numbers. For instance, s orbitals are spherical, p orbitals are dumbbell-shaped, d orbitals are mostly clover-shaped, and f orbitals are more complex.

In relation to the problem at hand, identifying the correct atomic orbital for an electron involves knowing the values of 'n' and 'l'. Atomic orbitals not only define where an electron can be found but also influence chemical bonding and the properties of elements.

Electron configuration details the arrangement of electrons in the atomic orbitals of an atom. It follows a set of principles: the Aufbau principle, the Pauli exclusion principle, and Hund's rule, which guide the order in which atomic orbitals are filled.

Electrons fill the lowest energy orbitals first before moving to higher ones (Aufbau principle). No two electrons in the same atom can have identical quantum numbers (Pauli exclusion principle), and single electrons with the same spin must occupy each equal-energy orbital before additional electrons with opposite spins can pair up (Hund's rule).

When determining which electron is at the highest energy level in a given atom, it's essential to consider the complete electron configuration, because electrons are added to the atom in order based on increasing energy levels. In the context of the exercise, knowing the electron configuration helps in understanding which electron is at the highest energy level by comparing their quantum numbers.