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Quantum numbers are crucial in determining the identity and behavior of electrons within an atom. They work together like a unique address for each electron, describing its specific energy state and position.

For each electron in an atom, there are four quantum numbers:

• **Principal quantum number** (\( n \)): indicates the main energy level or shell of an electron and can be any positive integer (1, 2, 3,...). For our problem, both electrons have \( n = 2 \).
• **Angular momentum quantum number** (\( \ell \)): describes the shape of the electron's orbital and ranges from 0 to \( n-1 \). Here, \( \ell = 1 \) corresponds to a p-type orbital.
• **Magnetic quantum number** (\( m_\ell \)): relates to the orientation of the orbital in space and ranges from \( -\ell \) to \( \ell \). Given \( \ell = 1 \), \( m_\ell \) can take the values \( -1, 0, \) or \( +1 \).
• **Spin quantum number** (\( m_s \)): indicates the electron's spin direction. Each electron can have a spin of \( +\frac{1}{2} \) or \( -\frac{1}{2} \).

By combining these quantum numbers, we define the exact state of each electron in an atom.

Electron configuration refers to the arrangement of electrons in the orbitals of an atom, which is organized by the aforementioned quantum numbers.

When determining the electron configuration, especially for more complex atoms, it is important to keep in mind:

• The **Aufbau principle**: Electrons fill orbitals starting at the lowest energy level before moving to higher ones.
• The **Pauli Exclusion Principle**: No two electrons can have the same set of all four quantum numbers in a single atom. Each electron in the same orbital must have opposite spins.
• **Hund’s Rule**: For orbitals of the same energy (degenerate orbitals), electrons fill each orbital singly before pairing up.

In our given scenario, knowing that the electrons have \( n = 2 \) and \( \ell = 1 \) situates them in the 2p subshell. Given the different possible values for \( m_\ell \) and the two possible spin states, electron configurations ensure electrons are spread according to these rules in a way that minimizes energy and respects quantum limitations.

In the quantum realm, particularly when considering particles like electrons, the concept of distinguishability becomes less intuitive. Electrons are considered indistinguishable because they do not have a unique identity - one electron is identical to another in every respect according to quantum mechanics.

For two electrons in the same atom with the same principal (\( n \)) and angular momentum quantum numbers (\( \ell \)), they can still be differentiated by their other quantum numbers (\( m_\ell \) and \( m_s \)). However, due to the Pauli Exclusion Principle, they cannot share the same quantum state entirely.

With indistinguishable particles like electrons, when calculating the number of possible states, it's important to account for the fact that exchanging two electrons does not lead to a new distinct state but rather the same physical state. As a result, you must consider symmetry and antisymmetry in quantum statistics. This is reflected in our calculation of quantum states, where identical configurations do not count as separate states.