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Q. 51

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Physics for Scientists and Engineers: A Strategic Approach with Modern Physics
Found in: Page 1138

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Short Answer

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

See the step by step solution

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

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