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Chapter 38: Q. 23 (page 1114)

What is the length of a one-dimensional box in which an electron in the n=1state has the same energy as a photon with a wavelength of 600nm?

Short Answer

Expert verified

The length of a one-dimensional box in which an electron in the n=1state has the same energy as a photon with a wavelength of 600nmisL=0.426nm

Step by step solution

01

Given Information

Electron in the n=1state has the same energy as a photon with a wavelength of 600nm

02

Calculation

We can start the solution by determining de Broglie wavelength

位=hmvv=hm位Ek=mv22Ek=mh22m2位2Ek=h22m位2Ek=6.63路10-3422路1.67路10-27路10路10-152Ek=1.3路10-12J=8.2MeV

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Most popular questions from this chapter

In the atom interferometer experiment of Figure 38.13, laser cooling techniques were used to cool a dilute vapor of sodium atoms to a temperature of 0.0010K=1.0mK. The ultracold atoms passed through a series of collimating apertures to form the atomic beam you see circling the figure from the left. The standing light waves were created from a laser beam with a wavelength of 590nm.

a. What is the rms speed vmeof a sodium atom (A-23)in a gas at temperature 1.0mK?

b. By treating the laser beam as if it were a diffraction grating. Calculate the first-order diffraction angle of a sodium atom traveling at the rms speed of part a.

c. how far apart are the points Band Cif the second sanding wave is 10cmfrom the first?

d. Because interference is observed between the two paths, each individual atom is apparently present at both points Band point CDescribe, in your own words, what this experiment tells you about the nature of matter.

A 100 W incandescent lightbulb emits about 5 W of visible light. (The other 95 W are emitted as infrared radiation or lost as heat to the surroundings.) The average wavelength of the visible light is about 600 nm, so make the simplifying assumption that all the light has this wavelength. How many visible-light photons does the bulb emit per second?

For what wavelength of light does a 100 mW laser deliver 2.50脳1017photons per second?

20.What is the quantum number of an electron confined in a 3.0-nm-long one-dimensional box if the electron's de Broglie wavelength is1.0nm ?

What is the radius of a hydrogen atom whose electron moves at7.3脳105m/s ?
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