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Q.36

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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 cm.

a. Determine the normalization constant c.

b. Draw a graph of c1x2 over the interval -2 cm x 2 cm. Provide numerical scales on both axes.

c. Draw a graph of 0 c1x2 0 2 over the interval -2 cm x 2 cm. Provide numerical scales.

d. If 104 electrons are detected, how many will be in the interval 0.00 cm x 0.50 cm?

(a) The value of normalization constant c is 0.866 cm-1/2

(d) prob =0.344

(e) The number of electrons detected in the interval

See the step by step solution

Step by Step Solution

Subpart (a) part 1:

Simplify it further and solve for c

Thus, the value of normalization constant c is 0.866 cm-1/2

Subpart (b) part 1:

The following is the graph of over the interval

From the above graph, it is clear that the values of decrease from position x=0cm to x=1cm so, the graph appears to be bowed upward in the interval and as per the condition, the value of is zero at

Subpart (c) part 1:

The following is the graph of over the interval

From the above graph, it is clear that the values of decrease from position x=0cm to x=1cm so, the graph appears to be bowed upward in the interval and as per the condition, the value of

Subpart (d) step 4:

Calculate the probability of electrons in the interval prob

=0.344

Given Expression:

Substitute 104 for N and 0.344 for

Thus the number of electrons detected in the interval 3440

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