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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The Frank Hertz experiment involved shooting electrons into a low density gas of mercury atoms and observing discrete amounts of kinetic energy loss by the electrons. Suppose that instead the similar experiment is done with a very cold gas of atomic hydrogen, so that all of the hydrogen atoms are initially in ground state. If the kinetic energy of an electron is 11.6 eV just before it collides with a hydrogen atom. How much kinetic energy will the electron have just after it collides with and excites the hydrogen atom?
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.)
The first excited state of a mercury atom is 4.9eV above the ground state. A moving electron collides with a mercury atom and excites the mercury atom to its first excited state. Immediately after the collision the kinetic energy of the electron is 0.3eV. What was the kinetic energy of the electron just before the collision?
If you double the amplitude, what happens to the frequency in a classical (non quantum) harmonic oscillator? In a quantum harmonic oscillator?
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: (green), (orange), and (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.
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