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Chapter 8: Q10P (page 344)
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?
The probability of staying atom in excited state is .
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If you double the amplitude, what happens to the frequency in a classical (non quantum) harmonic oscillator? In a quantum harmonic oscillator?
Suppose that a collection of quantum harmonic oscillators occupies the lowest four energy levels, and the spacing between levels is . 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.
At t =0 all of the atoms in a collection of 10000 atoms are in a excited state whose lifetime is 25 ns. Approximately how many atoms will still be in excited state at t= 12 ns.
Assume that a hypothetical object has just four quantum states, with the following energies:
(third excited state)
(second excited state)
(first excited state)
(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 “selection rules” 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 (“dark”) 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.
Match the description of a process with the corresponding arrow in figure 8.38: (a) Absorption of a photon whose energy is . (b) Absorption from an excited state (a rare event at ordinary temperatures). (c) Emission of a photon whose energy is . (d) Emission of a photon whose energy is . (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.
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