The electrons of the same orbitals can be distinguished by

The correct option is Spin quantum number.

To understand why this is the correct answer, let us break down how electrons in an atom are described using quantum numbers.

An electron in an atom is completely described by a set of four quantum numbers:

1. Principal Quantum Number (represented by the symbol $n$): This quantum number determines the main energy level or shell in which the electron resides. It can take positive integer values:
$n=1,2,3,...$

2. Azimuthal Quantum Number (also known as the Orbital Angular Momentum Quantum Number, represented by the symbol $l$): This quantum number defines the shape of the orbital or subshell. For a given shell $n$, $l$ can have integer values ranging from $0$ to $n-1$. Different values of $l$ correspond to different subshells, such as s, p, d, and f orbitals.

3. Magnetic Quantum Number (represented by the symbol $m_l$): This quantum number describes the spatial orientation of the orbital in space. For a given value of $l$, $m_l$ can range from $-l$ to $+l$, including zero. This defines the specific orbital within a subshell.

For example, if we consider a specific orbital, such as the $2p_x$ orbital, all electrons occupying this specific orbital will share the exact same values for these three quantum numbers:
$n=2$
$l=1$
$m_l=-1$ (or another specific value corresponding to $p_x$).

4. Spin Quantum Number (represented by the symbol $m_s$): According to the Pauli Exclusion Principle, no two electrons in the same atom can have the identical set of all four quantum numbers. Since an orbital can hold a maximum of two electrons, these two electrons must share the same $n$, $l$, and $m_l$. Therefore, to satisfy the Pauli Exclusion Principle, they must have opposite spins.

The spin quantum number can only have two possible values:
$m_s=+\frac{1}{2}$ (often represented as spin-up or ↑)
and
$m_s=-\frac{1}{2}$ (often represented as spin-down or ↓).

Consequently, the two electrons residing in the same orbital are distinguished solely by their spin quantum number.