The wave function for a particle in a box of length L is given by
)If the box extends from x = 0 to x = L,at which of the following positions is the highest probability for finding the particle?
A)x = 0.33 L
B)x = 0.04 L
C)x = 0.60 L
D)Both (a)and (b).
E)Both (b)and (c).

Question

The wave function for a particle in a box of length L is given by 
)If the box extends from x = 0 to x = L,at which of the following positions is the highest probability for finding the particle?
A)x = 0.33 L 
B)x = 0.04 L 
C)x = 0.60 L 
D)Both (a)and (b). 
E)Both (b)and (c).

Quizplus · Accepted Answer

The highest probability for finding the particle occurs at the position where the wave function is highest, which is at the peak of the curve. Taking the derivative of the wave function and setting it equal to zero, we find that the peak occurs at x = 0.60L. Choice A (x = 0.33L) and B (x = 0.04L) are not the positions of highest probability. Therefore, the best choice is C.

The Wave Function for a Particle in a Box of Length