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 probability density P(x) versus x is shown. The value of the quantum number n is:
A) 0
B) 1
C) 2
D) 3
E) 4

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 probability density P(x) versus x is shown. The value of the quantum number n is: 
A) 0 
B) 1 
C) 2 
D) 3 
E) 4

Quizplus · Accepted Answer

The probability density graph shows a clear pattern of peaks and nodes, which can be used to determine the quantum number n. Each peak corresponds to a maximum probability density, and each node corresponds to zero probability density. The number of peaks (excluding the one at x=0) corresponds to n-1, and the number of nodes corresponds to n. Therefore, in this case, there are 2 peaks, which corresponds to n-1=1, and there are 3 nodes, which corresponds to n=2. Thus, the answer is C, n=2.

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