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The Quantum Model

Shell K L M N
Sublevels 1s 2s 2p 3s 3p 3d 4s 3p 4d 4f
Maximum number of electrons 2 2 6 2 6 10 2 6 10 14
The principle quantum number, n, can have values 1, 2, 3, … and is indicative of the major energy levels of the electron in an atom in a gross way. This is similar to the quantum levels in Bohr’s theory. The azimuthal quantum number, l, has values from 0 to (n – 1), for each value of n. It is a measure of the angular momentum of the electron, which is Description: 14223.png in magnitude. Values of l = 0, 1, 2, 3, … and are designated by the letters s, p, d, f, …. The magnetic quantum number m is indicative of the component of the angular momentum vector in any one chosen direction, usually the z-axis. The values of m are from –l to +l including zero for any value of l. An electron can spin either in clockwise direction or in anticlockwise direction. Spin quantum number, s, can have two values + ½ and –½, which are also represented by arrow pointing in opposite directions, i.e., k and l, for any particular value of magnetic quantum number.

Node and nodal plane

Node is defined as a region where the probability of finding an electron is zero.
Nodes can be of two types: (i) radial node or spherical node and (ii) angular node or planar node.
  1. Radial node or spherical node: They correspond to n values, i.e., as the distance between nucleus and outermost shell increases, the number of radial nodes increases. For example, 1s, 2p, 3d, and 4f orbitals are closest to nucleus (since 1p, 1d, 2d, 1f, 2f, 3f do not exist), so there is no radial node. However, for higher values of n, radial nodes can be defined.
  2. Angular node or planar node: They correspond to l value. It depends on the shape of orbitals. For example, s orbitals are spherically symmetrical in all three planes; so in the s-orbital, no angular node exists. p-orbitals are not spherically symmetrical but the electron density is concentrated in one plane, either in x, y, or z. So they have one angular node. Similarly, electron density in d-orbital is concentrated in two planes, i.e., xy, yz, zx, etc. So the d-orbitals have two angular nodes.
    Total number of radial nodes = (nl – 1)
    Total number of angular nodes = l
    Total number of nodes = (nl – 1) + l = n – 1

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