Quantum number and their significance

Quantum number and their significance

1. Quantum numbers and their significance Dr. Mithil Fal Desai Shree Mallikarjun and Shri Chetan Manju Desai College Canacona Goa

2. Defining a state of an electron The wavefunctions obtained by solving the Schrodinger wave equation are labelled by three by a set of three integers termed as Quantum Numbers . Principal quantum number ‘n’ Subsidiary quantum number ‘l’ Magnetic quantum number ‘m l ’

3. Principal quantum number ‘n’ Energy and size = At n = 1, As n→∞, energy → zero (electron is stationary) n n = 1, 2, 3, …., ∞  

4. Subsidiary/Azimuthal quantum number ‘l’ Angular momentum and shape l = 0 l = 1 l = 2 l = 0, 1, 2, 3, …., (n-1) n = 1, l = 0 n = 2, l = 0, 1 n = 3, l = 0, 1, 2 l = 0 → s orbital (spherical) l = 1 → p orbital (dumbbell) l = 2 → d orbital (double dumbbell) l = 3 → f orbital

5. Magnetic quantum number ‘m l ’ Orientation of angular momentum l = 0 l = 1 x y z x y z m l = -l…,0,…+l l = 0 → m l = 0 (one orbital) l = l, → m l = -1, 0, +1 (three orbitals)