Which atom has the electron configuration \(1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 3 d^{7} 4 s^{2} ?\)

Quantum numbers play a critical role in understanding electron configurations and the behavior of electrons in an atom. They are essentially the 'address' of an electron, describing its location and movement within the atom. There are four quantum numbers:

• The principal quantum number (n) indicates the energy level and size of the orbital where the electron is likely to be found. It can be any positive integer starting from 1.
• The angular momentum quantum number (l) specifies the shape of the orbital and is dependent on the value of the principal quantum number. Its value ranges from 0 to n-1.
• The magnetic quantum number (m_l) indicates the orientation of the orbital in space relative to the other orbitals and can take on values from -l to +l.
• The spin quantum number (m_s) represents the spin direction of the electron, which can be either +1/2 or -1/2.

In our exercise example, the highest principal quantum number identified is 4, which tells us we are dealing with orbitals within the fourth energy level.

In the world of atomic structure, orbitals are described as regions where there is a high probability of finding an electron. There are various orbital types, each with a unique shape and electron capacity:

• The s orbitals are spherical and can hold up to two electrons.
• The p orbitals have a dumbbell shape and can hold up to six electrons, with two electrons in each of the three orientations.
• The d orbitals are more complex in shape and can hold up to ten electrons.
• There are also f orbitals, which can fill up to fourteen electrons, but they are not involved in the given electron configuration.

In the exercise configuration, when we encounter the term '3d⁷', it indicates there are seven electrons within the five d orbitals at the third energy level.

The periodic table is an organized chart that illustrates the chemical elements arranged by their atomic numbers, electronic configurations, and chemical properties. Its structure helps predict how elements will react with each other. Elements are arranged in order of increasing atomic number from left to right and divided into periods (rows) and groups (columns).

Using the periodic table, we link the total number of electrons to their corresponding element. In our solution, we counted 27 electrons, which we can then match to the atomic number of cobalt (Co). Cobalt resides in the eighth group (known as the transition metals) and the fourth period, consistent with its 4s² electron configuration.