Two electrons occupying the same orbital are distinguished by

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two electrons occupying the same orbital are distinguished by

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Two electrons occupying the same orbital are distinguished by

Answer:
Two electrons occupying the same orbital are distinguished by their spin quantum numbers. According to the Pauli Exclusion Principle, no two electrons in an atom can have the same set of four quantum numbers. These four quantum numbers are:

  1. Principal Quantum Number (n): Indicates the main energy level or shell.
  2. Angular Momentum Quantum Number (l): Indicates the shape of the orbital.
  3. Magnetic Quantum Number (mâ‚—): Indicates the orientation of the orbital around the nucleus.
  4. Spin Quantum Number (mₛ): Indicates the direction of the electron’s spin.

Explanation:

  1. Principal Quantum Number (n):

    • Defines the energy level and size of the orbital.
    • For example, ( n = 1, 2, 3, \ldots ).

  2. Angular Momentum Quantum Number (l):

    • Defines the shape of the orbital.
    • It ranges from ( 0 ) to ( n-1 ). For example, if ( n = 2 ), then ( l ) could be ( 0 ) or ( 1 ).

  3. Magnetic Quantum Number (mâ‚—):

    • Defines the orbital’s orientation in space.
    • It ranges from ( -l ) to ( +l ). For example, if ( l = 1 ), ( mâ‚— ) could be ( -1, 0, \text{or} 1 ).

  4. Spin Quantum Number (mâ‚›):

    • Indicates the direction of the electron’s spin.
    • It can only be ( +\frac{1}{2} ) or ( -\frac{1}{2} ).

Distinguishing Electrons in the Same Orbital:

For two electrons to occupy the same orbital, their first three quantum numbers (n, l, mâ‚—) must be identical. However, their spin quantum numbers (mâ‚›) must be different to satisfy the Pauli Exclusion Principle. This means one electron will have a spin quantum number of +\frac{1}{2} and the other will have -\frac{1}{2} .

Key Points:

  • Pauli Exclusion Principle: States that no two electrons in the same atom can have the same set of four quantum numbers.
  • Spin Quantum Number: The quality that distinguishes two electrons in the same orbital.

Solution By Steps:

  1. Same Orbital:

    • Electrons have the same principal, angular momentum, and magnetic quantum numbers (n, l, mâ‚—).

  2. Different Spins:

    • Their spin quantum numbers (mâ‚›) must differ.
    • One electron: mâ‚› = +\frac{1}{2}
    • Other electron: mâ‚› = -\frac{1}{2}

Final Answer:
Two electrons occupying the same orbital are distinguished by their spin quantum numbers (mâ‚›).

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