Question

1. Calculate the probability of locating an electron in a one-dimensional box of length 2.00 nm and n_x=4 between 0 and 0.286 nm. The probability is also plotted. You should compare (qualitatively) your numerical answer to the area under the curve on the graph that corresponds to the probability.

Answer 1

Given data:

Length of the box (a)= 2.00 nm

n_x= 4

We know that probability of locating an electron in 1D box is:

Where x and y are the positions in between of which the probability of electron is to be calculated ( 0 and 0.286 nm here)

a is the length of the box

n_xis the principal quantum number along x axis

In the above formula the quantity inside | | is called the wave function of electron which has form:

Substituting values in the formula mentioned in the beginning we get:

Taking the constant terms outside the integration sign:

Upon solving above integral we get (I've used Wolfram Alpha):

Which is the required answer

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