Question

Draw the following orbitals according to the radial and angular variations of the wavefunction, including phases. Indicate the number of both radial and angular nodes for each orbital. Add axes, if appropriate.

a) 4p_x b) 6s c) 6d_xz d) 5f_z3

Answer 1

Angular nodes fpr particular orbital is constant and it does not depend on principal quantum number.

Angular nodes for s orbital = 0

for p orbital = 1

for d orbital = 2

for f orbital = 3

for g orbital = 4

and so on

radial nodes for s orbital = n - 1 (where n is principal quantum number)

  for p orbital = n - 2

  for d orbital = n - 3

  for f orbital = n - 4

  for g orbital = n - 5

and so on

a) 4px has 2 radial and 1 angular nodal plane

Total nodes for 4px orbital = 2+1

= 3

radial probability densities for 4px it has two radial nodes.

b) 6s has 5 radial and 0 angular nodal plane

Total nodes for 6s orbital = 5+0

= 5

c) 6dxz has 3 radial and 2 angular nodal plane

Total nodes for 6dxz orbital = 3+2

= 5

d) 5fz³ has 1 radial and 3 angular nodal plane

Total nodes for 5fz³ orbital = 1+3

= 4

as shown above diagram we can draw the radial probability densities for remaining orbitals also.