Question:
Which of the following quantum numbers determines the shape of an orbital?
Which of the following quantum numbers determines the shape of an orbital?
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Remember, \( l = 0 \) for s-orbitals, \( l = 1 \) for p-orbitals, and so on. This helps in visualizing the basic shapes associated with different values of \( l \).
Updated On: Jun 3, 2026
- Azimuthal quantum number
- Principal quantum number
- Magnetic quantum number
- Spin quantum number
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The Correct Option is A
Solution and Explanation
[5pt]
Step 1: Concept
In atomic physics, electrons in atoms are described by four quantum numbers: the principal quantum number ($n$), the azimuthal quantum number ($l$), the magnetic quantum number ($m_l$), and the spin quantum number ($m_s$). These quantum numbers provide information about the energy level, shape, orientation, and spin of an electron's orbital.
[5pt]
Step 2: Meaning
The principal quantum number $n$ determines the main energy level or shell of the electron.
The azimuthal quantum number $l$ specifies the type of orbital (s, p, d, f).
The magnetic quantum number $m_l$ indicates the orientation of the orbital in space.
The spin quantum number $m_s$ describes the intrinsic angular momentum of the electron.
[5pt]
Step 3: Analysis
To determine which quantum number decides the shape of an atomic orbital, we need to understand what each quantum number represents:
The principal quantum number $n$ only determines the energy level and size of the orbital.
The magnetic quantum number $m_l$ describes how the orbital is oriented in space but does not define its shape directly.
The spin quantum number $m_s$ deals with the electron's intrinsic angular momentum, which does not affect the shape or orientation of the orbital.
[5pt] The azimuthal quantum number $l$, however, plays a crucial role. It defines the shape of the atomic orbital:
For $l = 0$, the orbital is spherical (s-orbital).
For $l = 1$, the orbital has a dumbbell shape (p-orbital).
For $l = 2$, the orbital can have more complex shapes like cloverleaf or double dumbbell (d-orbital).
Step 4: Conclusion
The quantum number that determines the shape of an atomic orbital is the azimuthal quantum number.
Final Answer: (A)
In atomic physics, electrons in atoms are described by four quantum numbers: the principal quantum number ($n$), the azimuthal quantum number ($l$), the magnetic quantum number ($m_l$), and the spin quantum number ($m_s$). These quantum numbers provide information about the energy level, shape, orientation, and spin of an electron's orbital.
[5pt]
Step 2: Meaning
The principal quantum number $n$ determines the main energy level or shell of the electron.
The azimuthal quantum number $l$ specifies the type of orbital (s, p, d, f).
The magnetic quantum number $m_l$ indicates the orientation of the orbital in space.
The spin quantum number $m_s$ describes the intrinsic angular momentum of the electron.
[5pt]
Step 3: Analysis
To determine which quantum number decides the shape of an atomic orbital, we need to understand what each quantum number represents:
The principal quantum number $n$ only determines the energy level and size of the orbital.
The magnetic quantum number $m_l$ describes how the orbital is oriented in space but does not define its shape directly.
The spin quantum number $m_s$ deals with the electron's intrinsic angular momentum, which does not affect the shape or orientation of the orbital.
[5pt] The azimuthal quantum number $l$, however, plays a crucial role. It defines the shape of the atomic orbital:
For $l = 0$, the orbital is spherical (s-orbital).
For $l = 1$, the orbital has a dumbbell shape (p-orbital).
For $l = 2$, the orbital can have more complex shapes like cloverleaf or double dumbbell (d-orbital).
Step 4: Conclusion
The quantum number that determines the shape of an atomic orbital is the azimuthal quantum number.
Final Answer: (A)
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