Answer to Question #100871 in Physical Chemistry for Mary

Question

By considering the radial wavefunctions of the 2s and 3s orbitals of hydrogen, a) deduce the number of nodes for each, and b) their location(s).

Answer 1

Solution.

a)

We can find the number of nodes according to this formula:

$N = n-l-1$

l = 0.

1)n=2

N = 1

2)n=3

N=2

b)

1)n=2

b)

Nodes are points (or surfaces) where the function R(r) is zero. On the graph of the dependence of the energy level on the distance to the core, they are shown as points of intersection with the x-axis.

Answer:

a)

N (n=2) = 1

N (n=3) = 2

b)

Nodes are points (or surfaces) where the function R(r) is zero. On the graph of the dependence of the energy level on the distance to the core, they are shown as points of intersection with the x-axis.