Atomic orbitals: 6s radial distribution function

Schematic plot of the 6s radial distribution function 4πr2ψ1s2

Schematic plot of the 6s orbital radial distribution function.

For s-orbitals, the radial distribution function is given by multiplying the electron density by 4πr2. By definition, it is independent of direction. In the case of the hydrogen atom, the maximum value of the radial distribution function corresponds to r = 1 AU, 52.9 pm.

The 6s radial distribution function has four spherical nodes but the higher s orbitals have more. The number of nodes is related to the principal quantum number, n. In general, the ns orbital have (n - 1) radial nodes. Therefore, the 6s-orbital has (6 - 1) = 5 radial nodes, as shown in the above plot. Additional radial nodes become evident in higher s-orbitals ( 7s) while lower orbitals ( 1s, 2s, 3s, 4s, 5s, 6s, and) have fewer.

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