A subshell n = 5, l = 3 can accommodate :
A subshell n = 5, l = 3 can accommodate :
A
10electrons
B
14 electrons
C
18 electrons
D
None of these
Text Solution
AI Generated Solution
The correct Answer is:
To determine how many electrons a subshell with principal quantum number \( n = 5 \) and azimuthal quantum number \( l = 3 \) can accommodate, we can follow these steps:
### Step-by-Step Solution:
1. **Identify the Quantum Numbers**:
- The principal quantum number \( n \) is given as 5.
- The azimuthal quantum number \( l \) is given as 3.
2. **Determine the Number of Orbitals**:
- The number of orbitals in a subshell can be calculated using the formula:
\[
\text{Number of orbitals} = 2l + 1
\]
- Substituting \( l = 3 \):
\[
\text{Number of orbitals} = 2(3) + 1 = 6 + 1 = 7
\]
3. **Identify the Type of Subshell**:
- The value of \( l \) corresponds to different types of orbitals:
- \( l = 0 \) corresponds to s orbitals
- \( l = 1 \) corresponds to p orbitals
- \( l = 2 \) corresponds to d orbitals
- \( l = 3 \) corresponds to f orbitals
- Since \( l = 3 \), this indicates that we are dealing with an f subshell.
4. **Calculate the Total Electron Capacity**:
- Each orbital can accommodate a maximum of 2 electrons.
- Therefore, the total number of electrons that can be accommodated in the subshell is:
\[
\text{Total electrons} = \text{Number of orbitals} \times 2 = 7 \times 2 = 14
\]
5. **Conclusion**:
- The subshell with \( n = 5 \) and \( l = 3 \) can accommodate a total of 14 electrons.
### Final Answer:
The subshell \( n = 5 \), \( l = 3 \) can accommodate **14 electrons**.
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