Radial and angular parts wave function

1. Radial and angular parts of the hydrogenic wave
functions, variations for 1s, 2s, 2p, 3s, 3p and 3d
orbitals ?
Mr. Mithil Fal Desai, Ph. D.
Assistant Professor in Chemistry
Shree Mallikarjun and Shri Chetan Manju Desai College
Canacona, Goa

2. 𝐝 𝟐
𝛙
𝐝𝐱 𝟐
+
𝐝 𝟐
𝛙
𝐝𝐲 𝟐
+
𝐝 𝟐
𝛙
𝐝𝐳 𝟐
+
𝟖𝛑 𝟐
𝐦
𝐡 𝟐
(𝐄 − 𝐕) = 𝟎
-----------1
Schrodinger equation with Cartesian coordinates

3. Cartesian coordinates and Polar coordinates
θ
φ r
(x, y, z) or (r, θ, φ)
x axis
zaxis
x = r sin θ cos ϕ
y = r sin θ sin ϕ
z = r cos θ
m = μ

4. 𝟏
𝐫 𝟐
𝐝
𝐝𝐫
(𝐫 𝟐
𝐝𝛙
𝐝𝐫
) +
𝟏
𝐫 𝟐 𝐬𝐢𝐧 𝛉
𝐝
𝐝𝛉
(𝐬𝐢𝐧 𝛉
𝐝𝛙
𝐝𝛉
) +
𝟏
𝐫 𝟐 𝐬𝐢𝐧 𝟐 𝛉
𝐝 𝟐 𝛙 𝟐
𝐝𝛟 𝟐
+
𝟖𝛑 𝟐 𝛍
𝐡 𝟐
(𝐄 − 𝐕) = 𝟎
-----------2
𝛙(r, 𝛉, 𝛟) = R(r), Θ(𝛉), Φ(𝛟)
𝛙(r, 𝛉, 𝛟) = R(r), Y(𝛉, 𝛟)
Schrodinger equation with polar coordinates
We have,

5. 𝛙(r, 𝛉, 𝛟) = R(r), Y(𝛉, 𝛟)
𝛙n𝐥𝐦𝐥 = Rnl(r), Ylm(𝛉, 𝛟)
Schrodinger equation with polar coordinates
We have,

6. Radial component ‘R(r)’ of wave function ′𝛙’ gives the distribution of
electron as a function of radius ‘r’(distance from the nucleus)
Radial wave function = R(r)
Radial component of wave function
Radial wave function depends on principle quantum number ‘n’ and
azimuthal quantum number ‘l’ and have a common function.

7. Angular component ‘Y(𝛉, 𝛟)’ of wave function ′𝛙’ gives the distribution of
electron as a function of angle (𝛉, 𝛟).
Angular component of wave function = Y(𝛉, 𝛟)
Angular component of wave function
Angular component depends on azimuthal quantum number ‘l’ and
magnetic quantum number.

8. 8
http://web.pdx.edu/~pmo
eck/lectures/modern/TRM
-7.ppt
Wave function
of Hydrogen
atom

9. Radial variation of wave function
Plot the graph of R(r) v/s r for
1s, 2s, 3s, 3p and 3d orbital

10. Angular variation of atomic orbital