A Particle is moving in one dimensional potential box (of infinite height) of width 25A' Calculate the probability of finding the particle within an interval of 5A' at the centre of the box when it is in its state of least energy.

 

Solution:

 Given-

 width of one dimensional potential box L=25A⁰

We know the normalized wave function for a particle in one dimensional potential box is

For Least energy n= 1, at the centre of box x = L/2

We know the probability of finding the particle in one dimensional box is given by

Where dx = interval =5A⁰