If a particle is confined to a one-dimensional box of length 300 pm, for $\Psi$₃ the particle is most likely to be found at A) 0 pm. B) 50, 150, and 250 pm, respectively. C) 17.3 pm. D) 300 pm. E) 100 and 200 pm, respectively.

Question

Quizplus · Accepted Answer

The probability density for a particle in a one-dimensional box is given by the equation: 
P(x) = (2/L)sin^2 (n*pi*x/L), where L is the length of the box and n is the quantum number. 
For the given wave function, n = 1, so the probability density function for the particle is: 
P(x) = (2/300)sin^2 (pi*x/300) 
The maximum values of sin^2 function occur at x = 50 pm, 150 pm and 250 pm, respectively. Therefore, the particle is most likely to be found at these positions.

If a Particle Is Confined to a One-Dimensional Box of Length