Question

explain the significance of 3 quantum numbers in predicting the positions of an election in an atom

Answer 1

The main significance of quantum numbers are

1. To determine size, distance from nucleus and energy of electron in orbit
2. To decide shape, energy of electron in sub orbit
3. To find number of orbitals and their directional position or orientation in space.
4. To find number of electrons and their spin.

​​1. Principal Quantum number:
This is used to specify the position and energy of the electron in an orbit or shell. This is denoted by n.
n = 1, 2, 3 ….
2. Angular momentum Quantum numbers:
This is also called subsidiary or azimuthal quantum number, denoted by l.
l = 0, 1, 2, 3 …. (n – 1)
This is used to describe subshell
l = 0, 1, 2, 3, 4, 5…..
Subshell = s, p, d, f, g…..
Where s, p, d, f, g…. are the symbols for sharp, principle, diffused, fundamental, degenerate spectral lines.
Any subshell is represented by n, l such that we write number for n and name for l.

• Total subshells in a shell is equal to numerical value of n.
• A subshell is possible only if l < n.
• l describes the shape of the orbital occupied by the electron.

l = 0 (s) – spherical
l = 1 (p) – dumb – bell
l = 2 (d) – double dumb – bell
3. ​Magnetic Quantum number:
This Quantum number denoted by ‘m’ determines orientation of orbitals in space.
m = – l to + l
Total value of m = 2l + 1
= no. of orbitals in a subshell

• Thus subshell (m = 0) will have one orbital.
• p subshell (m = -1, 0, +1) has three orbitals (p_x, p_y, p_z)
• d subshell (m = - 2, - 1, 0, +1, 2) has five orbitals (d_xy, d_yz, d_zx, d_z², d_x² _{- y}²). These are also equal in energy.
• Splitting (resolution) of spectrum lines occurs when placed in a magnetic field. (zeeman effect) or in an electric field (stark’s effect). Total lines form a single line in the normal spectrum = (2l + 1)

​​4. Spin Quantum number:
The electron can be regarded as spinning on its axis, like a top in a clockwise and anti – clockwise direction. This is called spin quantum number denoted by m_s.