Quantum Numbers

Question

The principal quantum number (n) primarily determines which property of an electron in an atom?

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1. **Principal Quantum Number ($n$)**: This number identifies the main energy shell to which an electron belongs.
2. **Physical Significance**: 
   - **Size**: As $n$ increases, the average distance of the electron from the nucleus increases, thus determining the **radial size** of the orbital.
   - **Energy**: For a hydrogen atom (or hydrogen-like species), $n$ is the sole determinant of orbital energy ($E_n \propto -1/n^2$). In multi-electron atoms, it still primarily determines the energy level.
3. **Other Quantum Numbers**:
   - **Azimuthal ($l$)**: Determines the **shape** of the orbital (s, p, d, f).
   - **Magnetic ($m_l$)**: Determines the **spatial orientation** of the orbital.
   - **Spin ($m_s$)**: Describes the intrinsic **spin** of the electron.

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