If spin quantum number has three values then how many electrons are possible in one orbital?

Question

Answer

3 electrons are possible

Answer

One orbital contain 3 electrons and 1s^3 is possible.
[ S = +1/2 , 0 , -- 1/2]

Answer

Now, each orbital can hold 3e−s each, so, total member of electrons is 3n2. So, 75 electrons totally.

Answer

Introduction:
The spin quantum number (s) is a fundamental property of electrons that describes their intrinsic angular momentum or 'spin.' It is denoted by the values +½ and -½, representing spin-up and spin-down states, respectively. The spin quantum number has three values because each electron orbital can accommodate a maximum of two electrons with opposite spins.

Explanation:
1. Spin and Pauli Exclusion Principle:
Electrons possess spin, which is a form of angular momentum. The Pauli Exclusion Principle states that no two electrons in an atom can have the same set of four quantum numbers. This principle is essential in determining the electron configurations and the arrangement of electrons in different orbitals.

2. Orbital and Electron Pairing:
An orbital is a region of space where there is a high probability of finding an electron. Each orbital can hold a maximum of two electrons, and they must have opposite spins (one up and one down). This pairing of electrons with opposite spins ensures the stability of the atom.

3. Spin Quantum Number and Electron Configuration:
The spin quantum number determines the orientation of an electron's spin within an orbital. It can take on only two values, +½ and -½, corresponding to the 'spin-up' and 'spin-down' states, respectively. The total number of possible spin states is given by 2s + 1, where s is the spin quantum number.

4. Maximum Number of Electrons in an Orbital:
Since each orbital can accommodate a maximum of two electrons with opposite spins, the maximum number of electrons in one orbital is 2.

5. Summary:
- The spin quantum number has three values: +½, 0, and -½.
- The spin-up and spin-down states correspond to the values +½ and -½, respectively.
- Each electron orbital can hold a maximum of two electrons with opposite spins.
- The maximum number of electrons in one orbital is 2.

Conclusion:
In summary, the spin quantum number has three values, but each orbital can only accommodate a maximum of two electrons with opposite spins. This principle contributes to the stability and organization of electron configurations within atoms, as dictated by the Pauli Exclusion Principle.

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