Explain QUANTAM NUMBERS [Atomic structure chemistry] class 11th
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Classical physics failed to explain atomic structure and electron behavior. Quantum numbers are mathematical parameters that describe the quantum state of electrons in atoms. There are four quantum numbers: n for principal, l for azimuthal, m-l for magnetic, and m-s for spin. These numbers completely specify an electron's state in an atom.
The principal quantum number n is the first and most important quantum number. It determines the energy level and size of electron orbitals. The values are positive integers: 1, 2, 3, 4, corresponding to electron shells K, L, M, N. Energy is inversely proportional to n squared, so higher n means higher energy and larger orbital size. Electrons in higher shells are farther from the nucleus.
The azimuthal quantum number l determines the shape of electron orbitals and defines subshells. Its values range from 0 to n minus 1. When l equals 0, we get s orbitals which are spherical. When l equals 1, we get p orbitals with dumbbell shapes. When l equals 2, we get d orbitals with complex shapes. When l equals 3, we get f orbitals with very complex shapes. Each subshell has different energy levels and angular momentum.
The magnetic quantum number m-l determines the orientation of orbitals in three-dimensional space. It ranges from negative l to positive l, including zero. For p orbitals where l equals 1, m-l can be negative 1, 0, or positive 1, corresponding to px, py, and pz orientations. The px orbital is oriented along the x-axis, py along the y-axis, and pz along the z-axis. The total number of orbitals for any subshell is 2l plus 1.
The spin quantum number m-s describes the intrinsic angular momentum of electrons. It has only two possible values: positive one-half and negative one-half, representing spin-up and spin-down electrons. The Pauli exclusion principle states that no two electrons can have identical sets of all four quantum numbers. This means a maximum of two electrons can occupy any orbital, and they must have opposite spins. Electron box diagrams show this with arrows pointing up and down.