To determine which orbital is not possible among the given options (2p, 3d, 3s, or 3f), we need to understand the structure of atomic orbitals and the rules governing their occupancy.
### Step-by-Step Solution:
1. **Understanding Principal Quantum Numbers**:
- The principal quantum number (n) indicates the energy level of an electron in an atom.
- For example, n=1 corresponds to the first energy level (K shell), n=2 to the second energy level (L shell), and n=3 to the third energy level (M shell).
2. **Maximum Electron Capacity**:
- The maximum number of electrons that can occupy a given energy level can be calculated using the formula \(2n^2\).
- For n=1 (K shell): \(2(1^2) = 2\) electrons.
- For n=2 (L shell): \(2(2^2) = 8\) electrons.
- For n=3 (M shell): \(2(3^2) = 18\) electrons.
3. **Subshells and Their Capacities**:
- Each energy level has subshells: s, p, d, and f.
- The capacities of these subshells are:
- s subshell can hold 2 electrons.
- p subshell can hold 6 electrons.
- d subshell can hold 10 electrons.
- f subshell can hold 14 electrons.
4. **Analyzing the Third Energy Level (n=3)**:
- In the third energy level (n=3), we can have:
- 3s: 2 electrons
- 3p: 6 electrons
- 3d: 10 electrons
- Total electrons that can be accommodated in the third shell: \(2 (from \, 3s) + 6 (from \, 3p) + 10 (from \, 3d) = 18\) electrons.
5. **Determining the Feasibility of 3f Orbital**:
- The 3f subshell would require additional electrons beyond the 18 already accounted for by the 3s, 3p, and 3d subshells.
- Therefore, the 3f subshell cannot exist in the third energy level because there is no capacity for it.
6. **Conclusion**:
- Among the options provided (2p, 3d, 3s, and 3f), the orbital that is not possible is **3f**.
### Final Answer:
The orbital that is not possible is **3f**.
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