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Chapter 8: Q22P (page 346)

A certain material is kept at very low temperature. It is observed that when photons with energies between 0.2 and 0.9 eV strike the material, only photons of 0.4 eV and 0.7 eV are absorbed. Next, the material is warmed up so that it starts to emit photons. When it has been warmed up enough that 0.7 eV photons begin to be emitted, what other photon energies are also observed to be emitted by the material? Explain briefly.

Short Answer

Expert verified

0.3 eV , 0.4 , and 0.7 eV

Step by step solution

01

Identification of the given data

The given data is listed below as,

  • The energies of the photons are 0.2eVand0.9eV.
  • The energies of the absorbed photons are 0.4eVand0.7eV.
  • The energy of the photons when emitted from the warmed material is0.7eV.
02

Significance of the law of Maxwell-Boltzmann distribution

The law of Maxwell-Boltzmann distribution states that energy distribution occurs only between the distinguishable and the identical particles.

The Maxwell-Boltzmann law gives the photon energies that are to be emitted by the material.

03

Determination of the photon energies emitted by the material

The detected lines of absorption at the energy of0.4eVand0.7eV provides the position of the 鈥渇irst two states of energy鈥� that is relative to the ground state. However, the absorbed photons take electrons from the ground state to different excited states.

While heating up the material, the electrons gain energy to move from the ground state to the other excited states and when the electrons come back to the ground states, the electrons emit photons.

As the law of Maxwell-Boltzmann distribution is mainly continuous, that shows some electrons will go to the first excited state that is0.4eV and some electrons will also go from the first to the second excited state that is 0.3eV.

Thus, the photon energies observed to be emitted by the material are0.3eV,04eVand0.7eV.

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Most popular questions from this chapter

Match the description of a process with the corresponding arrow in figure 8.38: (a) Absorption of a photon whose energy is E1-E0. (b) Absorption from an excited state (a rare event at ordinary temperatures). (c) Emission of a photon whose energy isE3-E1 . (d) Emission of a photon whose energy isE2-E0 . (e) In drawing arrows to represent energy transitions, which of the following statement are correct. (1) it doesn鈥檛 matter in which direction you draw the arrow as long as it connects the initial and final states. (2) For emission, the arrow points down. (3) For absorption, the arrow points up. (4) The tail of the arrow is drawn on the initial state. (5) The head of the arrow is drawn on the final state. (6) It is not necessary to draw and arrowhead.

Suppose we have a reason to suspect that a certain quantum object has only three quantum states.When we excite a collection of such objects we observe that they emit electromagnetic radiation of three different energies: 0.3鈥�eV(infrared), 2.0鈥�eV(visible), and 2.3鈥�eV(visible).

(a) Draw a possible energy-level diagram for one of the quantum objects, which has three bound states. On the diagram, indicate the transitions corresponding to the emitted photons, and check that the possible transitions produce the observed photons and no others. The energyK+U of the ground state is -4eV. Label the energies of each level ( K+U, which is negative).

(b) 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")? Energy of highest-energy dark line: eV Energy of lowest-energy dark line: eV

(c) There exists another possible set of energy levels for these objects which produces the same photon emission spectrum. On an alternative energy-level diagram, different from the one you drew in part (a), indicate the transitions corresponding to the emitted photons, and check that the possible transitions produce the observed photons and no others. When you are sure that your alternative energy-level diagram is consistent with the observed photon energies, enter the energies of each level (K+U, which is negative).

(d) For your second proposed energy-level scheme, what photon energies would be observed to be significantly reduced in intensity in an absorption experiment ("dark absorption lines")? (Given the differences from part (b), you can see that an absorption measurement can be used to tell which of your two energy-level schemes is correct).

Suppose that a collection of quantum harmonic oscillators occupies the lowest four energy levels, and the spacing between levels is 0.4鈥�eV. What is the complete emission spectrum for this system? That is, what photon energies will appear in the emissions? Include all energies, whether or not they fall in the visible region of the electromagnetic spectrum.

The mean lifetime of a certain excited atomic state is 5 ns. What is the probability of the atom staying in this excited state for t=10 ns or more?


Assume that a hypothetical object has just four quantum states, with the following energies:

-1.0eV(third excited state)

-1.8eV(second excited state)

-2.9eV(first excited state)

-4.8eV(ground state)

(a) Suppose that material containing many such objects is hit with a beam of energetic electrons, which ensures that there are always some objects in all of these states. What are the six energies of photons that could be strongly emitted by the material? (In actual quantum objects there are often 鈥渟election rules鈥� that forbid certain emissions even though there is enough energy; assume that there are no such restrictions here.) List the photon emission energies. (b) Next, suppose that the beam of electrons is shut off so that all of the objects are in the ground state almost all the time. If electromagnetic radiation with a wide range of energies is passed through the material, what will be the three energies of photons corresponding to missing (鈥渄ark鈥�) lines in the spectrum? Remember that there is hardly any absorption from excited states, because emission from an excited state happens very quickly, so there is never a significant number of objects in an excited state. Assume that the detector is sensitive to a wide range of photon energies, not just energies in the visible region. List the dark-line energies.
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