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Chapter 39: Q 7 Exercise (page 1136)

In one experiment, 2000 photons are detected in a 0.10-mm- wide strip where the amplitude of the electromagnetic wave is 10 V/m. How many photons are detected in a nearby 0.10-mm- wide strip where the amplitude is 30 V/m?

Short Answer

Expert verified

Therefore 18000 photons are detected in a nearby 0.10 mm wide strip.

Step by step solution

01

Given information

In one experiment, 2000 photons are detected in a 0.10-mm- wide strip where the amplitude of the electromagnetic wave is 10 V/m.

02

Explanation

Assume that f is the light's frequency and H is the strip's height. So we have:

f=HI(x)δxhN

We have the values as:

A=10V/m,thereforeI=100v2/m2andδx=0.10mm.N=2000

Therefore,

f=Hδx×100h×2000

The number of photons is:

N2=HδxIfhN2=Hδx900Hδx×100h×2000

Substituting the values.

N2=9001002000N2=18000

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Most popular questions from this chapter

3 shows the probability density for an electron that has passed through an experimental apparatus. What is the probability that the electron will land in a 0.010-mm-wide strip at (a) x = 0.000 mm, (b) x = 0.500 mm, (c) x = 1.000 mm, and (d) x = 2.000 mm?

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?

a. Starting with the expression ΔfΔt≈1for a wave packet, find an expression for the product ΔEΔtfor a photon.

b. Interpret your expression. What does it tell you?

c. The Bohr model of atomic quantization says that an atom in an excited state can jump to a lower-energy state by emitting a photon. The Bohr model says nothing about how long this process takes. You'll learn in Chapter 41 that the time any particular atom spends in the excited state before cmitting a photon is unprcdictablc, but the average lifetime Δtof many atoms can be determined. You can think of Δtas being the uncertainty in your knowledge of how long the atom spends in the excited state. A typical value is Δt≈10ns. Consider an atom that emits a photon with a 500nmwavelength as it jumps down from an excited state. What is the uncertainty in the energy of the photon? Give your answer in eV.

d. What is the fractional uncertainty ΔE/Ein the photon's energy?

A thin solid barrier in the xy-plane has a 10μmdiameter circular hole. An electron traveling in the zdirection with vx=0m/spasses through the hole. Afterward, is it certain that vxis still zero? If not, within what range is vxlikely to be?

1.0x 1010 photons pass through an experimental apparatus. How many of them land in a 0.10-mm-wide strip where the probability density is 20 m-1?
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