Question

The number of orbitals in a given subshell, such as the $5d$ subshell, is determined by the number of possible values of?
(A) $l$
(B) $n$
(C) $m_l$
(D) $m_s$

Answer 1

Hint: Quantum numbers are a set of numbers that describe the position and energy of an electron in an atom. Principal, azimuthal, magnetic, and spin quantum numbers are the four types of quantum numbers.

Complete answer:
The number of orbitals and their orientation in a given subshell are principally determined by the magnetic quantum number that is represented as $m_l$ . This value represents the projection of the orbital angular momentum along a specific axis.
It is determined by the azimuthal quantum number, which is also known as the orbital angular momentum quantum number.
As the magnetic quantum number is dependent on azimuthal quantum number, its value ranges from $-$ to $+$ , including $0$
The symbol ‘ $n$ ' stands for principal quantum numbers. They designate the atom's primary electron shell. Because it describes the most likely distance between the nucleus and the electrons, a bigger value of the primary quantum number denotes a greater distance between the nucleus and the electrons.
The form of an orbital is described by the azimuthal (or orbital angular momentum) quantum number. Its value is equal to the total number of angular nodes in the orbital and is indicated by the symbol ‘ $l$ ’.
The values of $n$ , $l$ , and $m_l$ have no effect on the electron spin quantum number. The symbol $m_s$ represents the value of this number, which indicates the direction in which the electron is spinning.
Hence, the correct option is C) $m_l$ .

Note:
According to Hund's laws, it is impossible for two electrons in the same atom to have the exact same quantum state or the exact same values of the set of quantum numbers. Three quantum numbers, the principal quantum number, azimuthal quantum number, and magnetic quantum number, are used to identify an orbital.