Q. 51

Expert-verifiedFound in: Page 1138

Book edition
4th

Author(s)
Randall D. Knight

Pages
1240 pages

ISBN
9780133942651

Consider the electron wave function

where 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

An electron wave function is given for the interval of ,

and for the interval of is, .

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

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

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:

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

The number of electrons detected is

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