Quantum Numbers
How many orbitals are present in the shell with principal quantum number n = 3?
Select the correct option:
Solution
9
- General Formula: The number of orbitals in a shell with principal quantum number n is given by n2.
- Subshell Analysis for n=3:
- For n=3, allowed values of l are 0,1,2.
- l=0 (3s subshell): 1 orbital (ml=0).
- l=1 (3p subshell): 3 orbitals (ml=−1,0,+1).
- l=2 (3d subshell): 5 orbitals (ml=−2,−1,0,+1,+2).
- Total Calculation: 1+3+5=9.
- Quick Check: 32=9.
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About This Question
- Subject
- chemistry
- Chapter
- atomic structure
- Topic
- quantum numbers
- Difficulty
- Easy
- Year
- 2025
Solution
Correct Answer:
9
- General Formula: The number of orbitals in a shell with principal quantum number n is given by n2.
- Subshell Analysis for n=3:
- For n=3, allowed values of l are 0,1,2.
- l=0 (3s subshell): 1 orbital (ml=0).
- l=1 (3p subshell): 3 orbitals (ml=−1,0,+1).
- l=2 (3d subshell): 5 orbitals (ml=−2,−1,0,+1,+2).
- Total Calculation: 1+3+5=9.
- Quick Check: 32=9.
This easy difficulty chemistry question is from the chapter atomic structure, covering the topic of quantum numbers. It appeared in the 2025 exam.
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