Question

The minimum number of quantum numbers required to specify an orbital in an atom is

• A. 1
• B. 4
• C. 2
• D. 3

Hint:

Remember that to define an orbital, you need three quantum numbers: \( n \), \( l \), and \( m_l \).

Answer 1

The Correct Option is D

To specify an orbital in an atom, three quantum numbers are required:
1. Principal quantum number (\( n \)): Specifies the energy level.
2. Azimuthal quantum number (\( l \)): Specifies the shape of the orbital.
3. Magnetic quantum number (\( m_l \)): Specifies the orientation of the orbital.
These three quantum numbers are sufficient to describe an orbital completely.
Thus, the minimum number of quantum numbers required to specify an orbital is \( \boxed{3} \).

Answer 2

Step 1: Understand what an orbital is.
An orbital is a region in an atom where the probability of finding an electron is maximum.
Each orbital is uniquely defined by a set of quantum numbers.

Step 2: Quantum numbers involved in defining an orbital.
There are four quantum numbers in total:
- Principal quantum number (\(n\)) – indicates the energy level or shell.
- Azimuthal quantum number (\(l\)) – indicates the subshell or shape of the orbital.
- Magnetic quantum number (\(m_l\)) – indicates the orientation of the orbital in space.
- Spin quantum number (\(m_s\)) – describes the spin of the electron, but not the orbital itself.

Step 3: Minimum number required to specify an orbital.
To specify an orbital (not the electron), we only need:
- \(n\) (principal),
- \(l\) (azimuthal), and
- \(m_l\) (magnetic).
These three quantum numbers are sufficient to identify a unique orbital.

Step 4: Conclusion.
The minimum number of quantum numbers required to specify an orbital in an atom is 3.