An electron is in a one-dimensional trap with zero potential energy in the interior and infinite potential energy at the walls. A graph of its wave function $\Psi$(x) versus x is shown. The value of quantum number n is:
A) 0
B) 1
C) 4
D) 6
E) 8

Question

An electron is in a one-dimensional trap with zero potential energy in the interior and infinite potential energy at the walls. A graph of its wave function $\Psi$(x) versus x is shown. The value of quantum number n is: 
A) 0 
B) 1 
C) 4 
D) 6 
E) 8

Quizplus · Accepted Answer

In a one-dimensional trap with zero potential energy in the interior and infinite potential energy at the walls, the wave function of the electron must be zero at the walls. This condition is fulfilled by standing waves, which have nodes (points where the wave function is zero) at the walls. The number of nodes in the wave function is equal to the quantum number n.

From the graph, we can see that the wave function has 4 nodes, 2 at each wall. Therefore, the value of quantum number n is 4.

An Electron Is in a One-Dimensional Trap with Zero Potential Ψ\PsiΨ

An Electron Is in a One-Dimensional Trap with Zero Potential $\Psi$