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Chapter 8: Q15P (page 344)

Suppose we have reason to suspect that a certain quantum object has only three quantum states. When we excite such an object we observe that it emits electromagnetic radiation of three different energies: 2.48eV(green), 1.91eV(orange), and 0.57eV(infrared). (a) Propose two possible energy-level schemes for this system. (b) Explain how to use an absorption measurement to distinguish between the two proposed schemes.

Short Answer

Expert verified

a) The value two possible energy levels 0.57eVand 1.34eV.

b) According to the energy absorbed by the lines.

Step by step solution

01

Identification of given data

Energies

2.48eV1.91eV0.57eV
02

Calculation of the possible energy level 

(a) We have three different energy levels

E1=2.48eVE2=1.91eVE3=0.57eV

E2-E1=2.48-1.91=0.57eV

E2-E1=1.91-0.57=1.34eV

03

Explanation

Absorption measurement is done with the help of using dark colour lines in the spectrum which means that the energy level absorbed by the lines will show their light and dark colour.

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Most popular questions from this chapter

Summarize the differences and similarities between different energy levels in a quantum oscillator. Specifically for the first two levels in figure 8.26, compare the angular frequency Ks/m, the amplitude , and the kinetic energyk at the same value of . ( In a quantum-mechanical analysis the concepts of angular frequency and amplitude require reinterpretation. Nevertheless, there remain elements of the classical picture. For example, larger amplitude corresponds to a higher probability of observing a large stretch.)

If you double the amplitude, what happens to the frequency in a classical (non quantum) harmonic oscillator? In a quantum harmonic oscillator?

When starlight passes through a cold cloud of hydrogen gas, some hydrogen atoms absorb energy, then reradiate it in all directions. As a result, spectrum of the star shows dark absorption lines at the energies for which less energy from the star reaches us. How does the spectrum of dark absorption lines for very cold hydrogen differs from the spectrum of bright emission lines from very hot hydrogen?

Some material consisting of a collection of microscopic objects is kept at a high temperature. A photon detector capable of detecting photon energies from infrared through ultraviolet observes photons emitted with energies of0.3eV,0.5eV,0.8eV,2,0eV,2.5eV,and2.8eV. These are the only photon energies observed. (a) Draw and label a possible energy-level diagram for one of the microscopic objects, which has four bound states. On the diagram, indicate the transitions corresponding to the emitted photons. Explain briefly. (b) Would a spring–mass model be a good model for these microscopic objects? Why or why not? (c) The material is now cooled down to a very low temperature, and the photon detector stops detecting photon emissions. Next, a beam of light with a continuous range of energies from infrared through ultraviolet shines on the material, and the photon detector observes the beam of light after it passes through the material. What photon energies in this beam of light are observed to be significantly reduced in intensity (“dark absorption lines”)? Explain briefly.

A hot bar of iron glows a dull red. Using our simple ball-spring model of a solid (Figure 8.23), answer the following questions,explaining in detail the processes involved. You will need to make some rough estimates of atomic properties based on prior work. (a) What is the approximate energy of the lowest-energy spectral emission line? Give a numerical value. (b) What is the approximate energy of the highest-energy spectral emission line? Give a numerical value. (c) What is the quantum number of the highest-energy occupied state? (d) Predict the energies of two other lines in the emission spectrum of the glowing iron bar. (Note: Our simple model is too simple-the actual spectrum is more complicated. However, this simple analysis gets at some important aspects of the phenomenon.)
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