Maximum Number of Electrons in Iron Atom with s1/2: An In-Depth Analysis

The spin quantum number, denoted as s, is one of the fundamental quantum numbers that describe the state of an electron in an atom. For an iron atom, determining the maximum number of electrons with a spin quantum number s1/2 requires understanding the electron configuration and the application of the Pauli exclusion principle.

Understanding the Electron Configuration of Iron

Iron (Fe) has an atomic number of 26, meaning it has 26 electrons. The electron configuration of iron is given by the notation:[Ar] 4s2 3d6This configuration indicates that there are 2 electrons in the 4s subshell and 6 electrons in the 3d subshell.

Role of the Spin Quantum Number in Electron Configuration

Each electron can have a spin quantum number of either 1/2 or -1/2. According to the Pauli exclusion principle, no two electrons in an atom can have the same set of four quantum numbers (n, l, m_l, m_s). The spin quantum number (m_s) is particularly important as it determines the orientation of an electron's spin angular momentum.

Electron Configuration and Spin in the 4s Subshell

4s Subshell

The 4s subshell contains 2 electrons. Both of these electrons can have a spin quantum number s 1/2, as each orbital can contain two electrons with opposite spins. Since there are no degenerate orbitals in the 4s subshell, both can have the s 1/2 state.

Electron Configuration and Spin in the 3d Subshell

3d Subshell

The 3d subshell contains 6 electrons. According to Hund's rule, electrons will fill degenerate orbitals singly before pairing up. This means that the maximum distribution would be:

3 electrons in 3d orbitals with s 1/2 3 electrons in 3d orbitals with s -1/2

Thus, up to 3 electrons in the 3d subshell can have a spin quantum number s 1/2.

Total Calculation

Adding the contributions from both subshells:

2 electrons in the 4s subshell with s 1/2 3 electrons in the 3d subshell with s 1/2

This gives a total of 5 electrons in the iron atom with a spin quantum number s 1/2.

Conclusion

The maximum number of electrons in an iron atom that can have a spin quantum number s 1/2 is 5. This is determined by the distribution of electrons in the 4s and 3d subshells according to the Pauli exclusion principle and Hund's rule.