Engineering Chemistry S Datta

10 ENGINEERING CHEMISTRY
Highlights:
l The probability of finding an electron at the origin is zero which is the nucleus.
This means the electron can never be at nucleus.
l The value of r which is the maximum probability in the graph of 1s distribution
agrees with the value of r of Bohr’s orbit of hydrogen atom (0.528Å).
l The distributions vary according to the principal quantum number. The larger the
value of the principal quantum number the farther is the electron from the nucleus
as the angular probability distribution remains uneffected by the value of principal
quantum number.
All these facts are based on the proper interpretation of Schrödinger wave equation.
Probability
1s
Probability
2s
r 0 1 2 Å
Distance r
(a)
0 r 1 2 r 2 4 6 8 Å
Distance r
(b)
Probability
2p
Probability
3s
0 2 4 6 8 Å
0 2 4 6 8 10 12 Å
Distance r
Distance r
(c)
(d)
Probability
3p
Probability
3d
Distance r
(e)
Distance r
(f)
Fig. 1.9 Radial probability distribution of 1s, 2s, 2p, 3s, 3p and 3d orbitals.