electrons move in circular orbits around the nucleus
C
electrons occupy orbitals of lowest energy
D
All the four quantum number of two electrons in an atom cannot be equal.
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**Step-by-Step Solution:**
1. **Understanding Pauli's Exclusion Principle**:
- Pauli's exclusion principle is a fundamental concept in quantum mechanics that applies to electrons in atoms. It states that no two electrons in the same atom can have the same set of four quantum numbers.
2. **Identifying the Four Quantum Numbers**:
- The four quantum numbers that describe the state of an electron in an atom are:
- \( n \) (Principal Quantum Number): Indicates the energy level or shell.
- \( l \) (Azimuthal Quantum Number): Indicates the subshell or shape of the orbital.
- \( m_l \) (Magnetic Quantum Number): Indicates the orientation of the orbital in space.
- \( m_s \) (Spin Quantum Number): Indicates the spin of the electron, which can be either +1/2 (up spin) or -1/2 (down spin).
3. **Application of the Principle**:
- For example, in a 2s orbital, which can hold a maximum of two electrons, the quantum numbers for these electrons can be described as follows:
- For the first electron (up spin):
- \( n = 2 \) (second shell)
- \( l = 0 \) (s orbital)
- \( m_l = 0 \) (only one orientation for s orbital)
- \( m_s = +1/2 \) (up spin)
- For the second electron (down spin):
- \( n = 2 \) (second shell)
- \( l = 0 \) (s orbital)
- \( m_l = 0 \) (only one orientation for s orbital)
- \( m_s = -1/2 \) (down spin)
4. **Conclusion**:
- According to the Pauli exclusion principle, while the first three quantum numbers (\( n \), \( l \), and \( m_l \)) can be the same for both electrons in the same orbital, the fourth quantum number (\( m_s \)) must differ. Therefore, the two electrons can coexist in the same orbital only if they have opposite spins.
**Final Statement**:
- Thus, Pauli's exclusion principle states that no two electrons in an atom can have the same set of all four quantum numbers.
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