In lecture 4 we have seen the functional forms of the orbitals of the hydrogen atom. The radial and angular parts of the orbitals are the solutions to the radial and angular parts of the
Schrödinger equation. In the present lecture, we will plot/sketch these orbitals to get a qualitative picture of the “shapes” and “sizes” of these orbitals.
Orbitals are the functions of the coordinates of one electron. These functions extend over the entire three dimensional space. The values of these functions (orbitals) are significant mainly in the small region of space (say, a volume of 5 x 5 x 57) around the nucleus. This does not mean that orbitals do not exist outside this volume.
Plots of the radial part of the orbitals of H-atom
In figure 5.1 we have shown the radial parts of hydrogenic orbitals. These are commonly written as Rnl (r). The distance from the nucleus is r, and n and l refer to the principal and angular momentum quantum numbers, respectively. When n = 1 and l = 0, it is the 1s orbital. This is an exponential function and it decays monotonically to zero from r = 0 to . The square of the radial part is also shown in an adjacent figure. If the 1s orbital decays with r as e - r , the square decays faster as e -2r .
The radial part of 2s (n = 2, l = 0 ) is shown in fig 5.1 . This function is the product of a linear function (2- ) and an exponential e - / 2 .
Here = 2 Zr / n a 0 . Here, a 0 is the Bohr radius, = 0.529 . In the previous lecture we used the symbol in place of . Both these represent a scaled distance r in units of na 0 / 2Z . We have deliberatively used alternative symbols so that the emphasis is on forms of the functions and not symbols. For < 2 , the function is positive, the function = 0 when = 2 and for >2, the function is negative and it asymptotically goes to zero . = 2 corresponds to the node (value of the wavefunction or the orbital = 0).
Figure 5.1 The radial parts of the orbitals for n = 1, 2, 3 and l = 0, 1 and 2. The squares of the orbitals are shown to the right.
. The square of the radial part is also shown in an adjacent figure. If the 1s orbital decays with r as e - r , the square decays faster as e -2r . 
) and an exponential e - 
/ 2 . 
= 2 Zr / n a 0 . Here, a 0 is the Bohr radius, = 0.529 
. In the previous lecture we used the symbol 
in place of 
< 2 , the function is positive, the function = 0 when 
>2, the function is negative and it asymptotically goes to zero . 
= 2 corresponds to the node (value of the wavefunction or the orbital = 0). 
