How do I sketch the wave functions of the 1s and 2s orbitals?
Hello! 🙂 I should understand the diagrams for these problems (a) and b). I also have the solutions. (See the second image opposite.) However, I'm not quite sure what the diagrams mean. Could someone explain the process to me and describe in detail how they were arrived at?
(Solutions)
Hopefully you know what the wave functions look like (only radial parts, unnored, in atomic units):
1s: ψ(r)=e ̄r
2s: ψ(r)=(2-r)e ̄2rᐟ2
2p: ψ(r)=r⋅e ̄rᐟ2
3s: ψ(r)=(27-18r+2r2)e ̄rᐟ3
3p: ψ(r)=(6-r)e ̄rᐟ3
3d: ψ(r)=r2⋅e ̄rᐟ3
And these are simply the functions that are plotted in the first row. In the second, you have the radial densities, i.e. the square of these times r2. The maxima in the densities correspond to the distances in which the electron is most common.
Thank you.