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Quantum Mechanical Model of Atom

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Estimated time: 6 minutes
Maharashtra State Board: Class 12

Key Points: Quantum Mechanical Model of Atom

Schrödinger Wave Equation:

Schrödinger developed the fundamental equation of quantum mechanics which incorporates the wave-particle duality of matter:

HΨ = EΨ

where H = Hamiltonian operator, Ψ (psi) = wave function, E = total energy of the system.

Quantum Numbers:

Four quantum numbers together describe the complete "address" of every electron in an atom:

Quantum Number Symbol What it describes Allowed Values
Principal n Shell size & energy level 1, 2, 3, 4, … (positive integers)
Azimuthal (Subsidiary) l 3D shape of orbital; angular momentum 0 to (n−1)
Magnetic Orbital mₗ Spatial orientation of orbital −l to +l (including 0)
Spin mₛ Direction of electron spin +½ (clockwise) or −½ (anticlockwise)

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