Question

Which of the following quantum numbers describes the spatial orientation of orbitals?

• A. n
• B. l
• C. m_l
• D. m_s

Answer 1

The Correct Option is C

To determine which quantum number describes the spatial orientation of orbitals, we need to understand the role of each quantum number in defining the properties of an electron in an atom.

1. Understanding Quantum Numbers:
There are four quantum numbers that describe the state of an electron in an atom:

1. Principal Quantum Number ($n$):
   This quantum number determines the main energy level or shell of the electron. It also gives information about the size and energy of the orbital. However, it does not describe the spatial orientation of the orbital.
2. Azimuthal Quantum Number ($l$):
   This quantum number determines the shape of the orbital (s, p, d, f). It specifies the subshell (e.g., $l = 0$ for s, $l = 1$ for p, etc.). While it provides information about the general shape, it does not directly describe the spatial orientation.
3. Magnetic Quantum Number ($m_l$):
   This quantum number determines the spatial orientation of the orbital within a given subshell. For example, in a p-subshell ($l = 1$), there are three possible orientations ($m_l = -1, 0, +1$), corresponding to the three p-orbitals ($p_x$, $p_y$, $p_z$). Thus, $m_l$ directly describes the spatial orientation of the orbital.
4. Spin Quantum Number ($m_s$):
   This quantum number describes the intrinsic spin of the electron. It can have two values: $+\frac{1}{2}$ or $-\frac{1}{2}$. It does not describe the spatial orientation of the orbital.

2. Identifying the Correct Quantum Number:
The question asks which quantum number describes the spatial orientation of orbitals. Based on the roles of the quantum numbers:

• $n$ determines the energy level but not the spatial orientation.
• $l$ determines the shape of the orbital but not its orientation.
• $m_l$ specifically describes the spatial orientation of the orbital.
• $m_s$ describes the spin of the electron, not the spatial orientation.

3. Conclusion:
The quantum number that describes the spatial orientation of orbitals is $m_l$.

Final Answer: $ {m_l} $