Question

In: Physics

1. Calculate the probability of locating an electron in a one-dimensional box of length 2.00 nm...

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.

Expert Solution

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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genius_generous answered 1 year ago

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