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Chapter 41: Q. 10 (page 1207)
Identify the element for each of these electron configurations. Then determine whether this configuration is the ground state or an excited state.
a.
b.
a. This configuration is for element Fluorine .
b. This configuration is for element Gallium.
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Identify the element for each of these electron configurations. Then determine whether this configuration is the ground state or an excited state.
a.
b.
Suppose you have a machine that gives you pieces of candy when you push a button. Eighty percent of the time, pushing the button gets you two pieces of candy. Twenty percent of the time, pushing the button yields pieces. The average number of pieces per push is . That is, pushes should get you, on average, pieces. Mathematically, the average value when the probabilities differ is . We can do the same thing in quantum mechanics, with the difference that the sum becomes an integral. If you measured the distance of the electron from the proton in many hydrogen atoms,
you would get many values, as indicated by the radial probability density. But the average value of would be
Calculate the average value of in terms of for the electron in the and the states of hydrogen.
A laser emits photons per second from an excited state with energy . The lower energy level is .
a. What is the wavelength of this laser?
b. What is the power output of this laser?
In fluorescence microscopy, an important tool in biology, a laser beam is absorbed by target molecules in a sample. These molecules are then imaged by a microscope as they emit longer-wavelength photons in quantum jumps back to lower energy levels, a process known as fluorescence. A variation on this technique is two-photon excitation. If two photons are absorbed simultaneously, their energies add. Consequently, a molecule that is normally excited by a photon of energycan be excited by the simultaneous absorption of two photons having half as much energy. For this process to be useful, the sample must be irradiated at the very high intensity of at least . This is achieved by concentrating the laser power into very short pulses ( pulse length) and then focusing the laser beam to a small spot. The laser is fired at the rate of pulses each second. Suppose a biologist wants to use two-photon excitation to excite a molecule that in normal fluorescence microscopy would be excited by a laser with a wavelength of . If she focuses the laser beam to a-diameter spot, what minimum energy must each pulse have?
What is the probability of finding a hydrogen electron at distance from the proton?
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