If a particle is confined to a one-dimensional box of length 300 pm,for $\varPsi$ ₃ the particle is most likely to be found at

Question

Quizplus · Accepted Answer

For a particle in a one-dimensional box in its ground state, the probability density function is given by:
P(x) = [(2/L)]*sin^2[(n*pi*x)/L]
Where L is the length of the box, n is the quantum number (n=1 for the ground state).
For this problem, L=300 pm, and n=1.
Therefore, P(x) = [(2/300 pm)]*sin^2[(pi*x)/300 pm]
The maximum value of sin^2[(pi*x)/300 pm] is 1, which occurs at x=50,150, and 250 pm. Therefore, the particle is most likely to be found at these positions, as stated in choice B.

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