13.0 Quantum Number

  Structure of Atom

• It determines the size and the energy of the orbital.
• n also tell about the number of shell.
• n can be any positive non-zero integer value.
• Greater the value of n farther is the electron from the nucleus.
• Each principal shell can accommodate a maximum of $2{n^2}$ electrons.
• Number of Orbitals in a shell is given by ${n^2}$.

Azimuthal Quantum Number(l)

• It is also known as orbital angular momentum or subsidiary quantum number.
• It defines shape of an orbital and number of subshells in a shell.
• It also represents angular momentum of an electron and it is given by$$\sqrt {l(l + 1)} \frac{h}{{2\pi }}$$
• Value of l has a range from 0 to (n-1).
• Value for l : 0 1 2 3 4 5 ...........
• notation for sub-shell: s p d f g h ............
• Number of subshells = n

Magnetic Quantum Number(${m_l}$)

• It tells about the orientation of the orbital in a co-ordinate system.
• For any given value of l, possible value of ml ranges from -l to l.
• Number of orbitals in a subshell = $(2l + 1)$
• Number of orbitals in a shell = ${n^2}$

Spin Quantum Number(${m_s}$)

• An electron spins about its own axis, either clockwise or anti-clockwise.
• Value of ${m_s}$ distinguish this two spins with the value of +1/2 or -1/2.
• ${m_s}$ defines the orientation of spin of an electron in an orbital.
• Maximum Number of electrons in a shell = $2{n^2}$