# 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, â€¦ 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 Bohrâ€™s theory. The azimuthal quantum number,*l*, has values from 0 to (*n*â€“ 1), for each value of*n*. It is a measure of the angular momentum of the electron, which is in magnitude. Values of*l*= 0, 1, 2, 3, â€¦ and are designated by the letters*s*,*p*,*d*,*f*, â€¦. 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 â€“*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 + Â½ and â€“Â½, 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.

Nodes can be of two types: (i) radial node or spherical node and (ii) angular node or planar node.

*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, 1*s*, 2*p*, 3*d*, and 4*f*orbitals are closest to nucleus (since 1*p*, 1*d*, 2*d*, 1*f*, 2*f*, 3*f*do not exist), so there is no radial node. However, for higher values of*n*, radial nodes can be defined.*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.*n*â€“*l*â€“ 1)*l*Total number of nodes = (*n*â€“*l*â€“ 1) +*l*=*n*â€“ 1