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Q.38

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Physics for Scientists and Engineers: A Strategic Approach with Modern Physics
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Short Answer

A particle is described by the wave function c1x2 = b cex/L x … 0 mm ce-x/L x Ú 0 mm where L = 2.0 mm.

a. Sketch graphs of both the wave function and the probability density as functions of x.

b. Determine the normalization constant c.

c. Calculate the probability of finding the particle within 1.0 mm of the origin. d. Interpret your answer to part b by shading the region representing this probability on the appropriate graph in part a

the normalization constant c is 0.707 mm-1/2

prob=

Thus the probability of finding the particle within 1.0mm for the origin is 63.2%

See the step by step solution

Step by Step Solution

To find the probability of  a particle

The expression for the probability of a particle at position x is given from probability density is as follows:

Here is the probability density

A particle is described by the wave function as follows:

Here L is 2.0nm

The probability density of the particle at is as follows:

The probability density of the particle at is as follows:

Table for the values of  and  is as follows:

(b)Determine the normalization constant csubstitute 2.0mm for LThus the normalization constant c is 0.707 mm-1/2

These are the constant

(c) Calculate the probability of finding the particle within 1.0mmof the origin.

Simplify the above equation furthersubstitute 2.0mm for L and 0.707 mm-1/2 for c

Thus the probability of finding the particle within 1.0mm for the origin is 63.2%

(d)The following is the graph showing the shaded region representing the finding of the particle within 1.0 mm of the origin.

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