Radial and angular parts wave function
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This document discusses the radial and angular parts of the hydrogenic wave functions for the 1s, 2s, 2p, 3s, 3p and 3d orbitals. It explains that the radial component, R(r), gives the distribution of the electron as a function of radius r from the nucleus. The angular component, Y(θ,φ), gives the distribution as a function of the angles θ and φ. It describes how R(r) depends on the principal and azimuthal quantum numbers, while Y(θ,φ) depends on the azimuthal and magnetic quantum numbers. Graphs are presented showing the radial variation of the wave functions for different orbitals.
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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.
- 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