Quantum Chemistry/Example 3

From Wikibooks, open books for an open world
Jump to navigation Jump to search

Write a question about calculating the number of nodes in a particle in a 1D box wavefunction.

Question 3[edit | edit source]

Calculate the number of nodes for a particle in a 1D box when n=2 and n=3 when the length of the box is L=5, and give the x-intercept of the node(s).

Wavefunction for a particle in a 1D-Box

Answer[edit | edit source]

Part 1[edit | edit source]



We're looking for one x-intercept.

Use the form where

is the x-intercept

x-intercepts are 0, , 5

0 and 5 are the edges of the box and is the only node.

Part 2[edit | edit source]



We're looking for two x-intercepts.

x-intercepts are

x-intercepts = 0,

0 and 5 are the edges of the box, and are the nodes.