00:01
Hello student, in this question we need to find a probability of finding a particle in a box of length l between 0 .25l and 0 .75l.
00:10
And we are given that the value of n, that is the state of the particle, is at 1.
00:15
So first of all, we need to know the sprodinger wave equation which tells the position of the particle at a particular point or a particular state.
00:24
So for a box of length l, for a box of length l, the position of the wave equation of the equation of the particle, which tells the position of the particle at a particular point at a particular state.
00:30
The particle which is denoted by z -i of n is given by root under 2 by l, where l is the length of the box multiplied by sine of n -pi x upon it.
00:49
So if the particle is at position x in the box, the box is of length l, then the position of the particle is found out zi by n.
00:59
And we need to find a probability.
01:03
And probability of a particle between the length l1 and l2 is denoted by integrating zi of n mod whole square l1 to l2, dx, where x is the dx is a small length we are traversing in the box.
01:29
Now if you apply this formula, then we will get probability.
01:33
Probability p is equal to integrating, we are, we need to find a probability between 0 .25l and 0 .75l.
01:43
So l1 will be 0 .25l and l2 will be 0 .75l.
01:50
Multiply by 2 by l.
01:55
We are squaring this xxxx.
01:58
Now, multiplied by xxx...