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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’t 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.

Short Answer

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Solution of the given question is shown in the below step in detail explanation.

Step by step solution

01

Concept Introduction

Whenever the bright lines fall on the metal surface, the emission of a photon takes place, and when the dark lines fall on the metal surface, the absorption of a photon takes place.

02

Explanation for (a)

Given that the photon is getting absorbed with the energy of E1−E0.

For the absorption process the tail of the arrow should be in the initial state and the head of the arrow should be in the final state. As here energy is E1−E0, so the tail of the arrow should be at E0 and the head of the arrow should be at E1.

Therefore absorption of photon whose energy isE1−E0 is represented by arrow 1.

03

Explanation for (b)

Given that absorption of photon takes place from an excited state (a rare event at low temperatures).

In the given diagram absorption of photon takes place from the excited state E1to E3.

Therefore the absorption from the excited state ( a rare event at low temperature) is represented by arrow .

04

Explanation for (c)

Given that the photon is getting emitted with the energy of E3−E1.

For the emission process the tail of the arrow should be in the initial state and the head of the arrow should be in the final state. As here energy is E3−E1, so the tail of the arrow should be at E3and the head of the arrow should be at E1.

Therefore, emission of photon whose energy is E3−E1is represented by arrow 2.

05

Explanation for (d)

Given that the photon is getting emitted with the energy of E2−E0.

For the emission process the tail of the arrow should be in the initial state and the head of the arrow should be in the final state. As here energy is E2−E0, so the tail of the arrow should be at E2 and the head of the arrow should be at E0.

Therefore emission of photon whose energy is E2−E0 is represented by arrow 3.

06

Explanation for  (e)

  1. In case of the absorption, the head of the arrow points up, whereas in case of emission the head of the arrow pints down. So the given statement is false.
  2. In case of emission the head of the arrow pints down. So the given statement is true.
  3. In case of the absorption, the head of the arrow points up. So the given statement is true.
  4. For the emission process the tail of the arrow should be in the initial state. So the given statement is true.
  5. For the emission or absorption, the head of the drawn to the final state. So the given statement is true.
  6. For the emission or absorption, the head of the drawn to the final state. If there is no error, so we can’t be able to find whether the transition is emission or absorption. So the given statement is false.

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Most popular questions from this chapter

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

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?

N=1 is the lowest electronic energy state for a hydrogen atom. (a) If a hydrogen atom is in a state N=4, what is K+U for this atom (in eV)? (b) The hydrogen atom makes a transition to state N=2, Now what is K+U in electron volts for this atom? (c) What is energy (in eV) of the photon emitted in the transition from level N=4 to N=2? (d) Which of the arrows in figure 8.40 represents this transition?

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 eV(infrared), 2.0 eV(visible), and 2.3 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 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.

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