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Chapter 39: Q 6 Exercise (page 1136)

In one experiment, 6000 photons are detected in a O.10-mm- wide strip where the amplitude of the electromagnetic wave is 200 V/m. What is the wave amplitude at a nearby 0.20-mm-wide strip where 3000 photons are detected?

Short Answer

Expert verified

Hence, the wave amplitude at 0.20mm wide strip is100V/m

Step by step solution

01

Given information

In one experiment, 6000 photons are detected in a O.10-mm- wide strip where the amplitude of the electromagnetic wave is 200 V/m.

02

Explanation

The first strip's photon count is given by

N1=HI1δx1hf(1) 

Count for second strip is:

role="math" localid="1648587585729" N2=HI2δx2hf(2)

Dividing (1) by (2):

N1N2=HI1δx1HI2δx2=I1δx1I2δx2

03

Calculations 

We have the values as:

N1=6000,n2=3000,I1=2002,I2=?,δx1=0.1mmandδx2=0.2mm

Substituting the values,

60003000=2002×0.1I2×0.2I2=100V/m

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Most popular questions from this chapter

What is the minimum uncertainty in position, in nm, of an electron whose velocity is known to be between 3.48×105m/sand 3.58×105m/s?

FIGURE Q39.1 shows the probability density for photons to be detected on thex-axis.

a. Is a photon more likely to be detected at x=0mor at x=1m ? Explain.

b. One million photons are detected. What is the expected number of photons in a 1−mm-wide interval at x=0.50m?

Physicists use laser beams to create an atom trap in which atoms are confined within a spherical region of space with a diameter of about 1mm. The scientists have been able to cool the atoms in an atom trap to a temperature of approximately 1nK, which is extremely close to absolute zero, but it would be interesting to know if this temperature is close to any limit set by quantum physics. We can explore this issue with a onedimensional model of a sodium atom in a 1.0-mm-long box.
a. Estimate the smallest range of speeds you might find for a sodium atom in this box.
b. Even if we do our best to bring a group of sodium atoms to rest, individual atoms will have speeds within the range you found in part a. Because there's a distribution of speeds, suppose we estimate that the root-mean-square speed vmsof the atoms in the trap is half the value you found in part a. Use this vrms to estimate the temperature of the atoms when they've been cooled to the limit set by the uncertainty principle.


FIGURE P39.32 shows |ψ(x)|2for the electrons in an experiment.

a. Is the electron wave function normalized? Explain.

b. Draw a graph of ψ(x)over this same interval. Provide a numerical scale on both axes. (There may be more than one acceptable answer.)

c. What is the probability that an electron will be detected in a 0.0010-cm-wide region at x=0.00cm? At x=0.50cm? At x=0.999cm?

d. If 104electrons are detected, how many are expected to land in the interval -0.30cm≤x≤0.30cm?

FIGURE P39.32 shows |ψ(x)|2for the electrons in an experiment.

a. Is the electron wave function normalized? Explain.

b. Draw a graph of ψ(x)over this same interval. Provide a numerical scale on both axes. (There may be more than one acceptable answer.)

c. What is the probability that an electron will be detected in a 0.0010-cm-wide region atx=0.00cm? At x=0.50cm? At x=0.999cm?

d. If 104electrons are detected, how many are expected to land in the interval -0.30cm≤x≤0.30cm?
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