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Q. 51

Expert-verified
Found in: Page 1138

### Physics for Scientists and Engineers: A Strategic Approach with Modern Physics

Book edition 4th
Author(s) Randall D. Knight
Pages 1240 pages
ISBN 9780133942651

# Consider the electron wave functionwhere x is in nm.a. Determine the normalization constant c.b. Draw a graph of over the interval .Provide numerical scales on both axes.c. Draw a graph of over the interval .Provide numerical scales.d. If electrons are detected, how many will be in the interval?

a. The value of normalization constant is

c. The number of electrons are detected in the given interval is

See the step by step solution

## Part a Step 1: Given data

An electron wave function is given for the interval of ,

and for the interval of is, .

## Step 2: Determination of the constant

Any wave function should satisfy the equation ,known as the normalization condition which is the probability of finding a particle at position .

Substituting the values of in the given interval, we get,

Therefore, the value of normalization constant is

## Part b Step 1: Graph of the wave function within

Plotting the values of wave function along y-axis and the position along x-axis we get the graph as:

## Part c Step 1: Graph of the probability density within

Within the given limit, we can write the probability density, substituting the value of normalization constant as,

when and

when

Therefore, the versus graph should be as following:

## Part d Step 1: Determination of the number of electron within

The probability of electron density within the given limit can be written as,

The number of electrons detected is