Question

Two electrons occupying the same orbital are distinguished by:
A. Principal quantum number
B. Magnetic quantum number
C. Azimuthal quantum number
D. Spin quantum number

Answer 1

Hint: We know the four types of quantum numbers are principal, azimuthal, magnetic and spin quantum numbers. And the values of these numbers depend on the position, shape or direction of the electrons and orbitals.

Step by step answer: For answering this question we need to know the four types of quantum numbers in detail.
So, a quantum number is a set of numbers used to describe the position and energy of the electron in an atom. Principal quantum number is denoted by $n$ , azimuthal by $l$ and which is also called orbital angular momentum quantum number, magnetic by $m$ and spin by ${m_s}$ .
Principal quantum number denotes the probable distance between the nucleus and the electrons is described by it. Larger the value of the principal quantum number means greater distance between the electron and the nucleus. The value of this number is always positive.
Azimuthal Quantum number or Orbital Angular Momentum Quantum number describes the shape of a given orbital. Its value is equal to the total number of angular nodes in the orbital. Value of this number indicates either an s, p, d or f subshell which vary in shapes.
Magnetic quantum number determines the total number of orbitals in a subshell and the orientation of the orbitals. This number yields the projection of the angular momentum corresponding to the orbital along a given axis. It is dependent on the value of azimuthal quantum number.
Spin quantum number is independent of the values of other three numbers. This value gives the idea into the direction in which the electron is spinning. The possible values here are $ + 1/2$ and $ - 1/2$ . The positive value implies upward spin on the electron or ‘spin up’ and negative value denotes downward spin or ‘spin down’.
Now, according to the question, we need to know how two electrons in the same orbital would be distinguished. Spin quantum number will distinguish these two electrons. As these two electrons are in the same orbital, the other three values would be the same. Therefore, spin quantum numbers will distinguish between them as one will have $ + 1/2$ and the other will have $ - 1/2$ spin quantum number.

Therefore, the correct answer is option D.

Note: The principal quantum number depends on the distance between the electron and nucleus. The azimuthal quantum number depends on the shape of the orbital. The magnetic quantum number depends on the number and orientation of orbitals. And spin quantum number depends on direction in which electron is spinning