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Chapter 41: Q. 1 (page 1206)
List the quantum numbers, excluding spin, of
(a) all possible states and
(b) all possible states.
(a) All possible states are
(b) All possible states are
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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.
Two excited energy levels are separated by the very small energy difference . As atoms in these levels undergo quantum jumps to the ground state, the photons they emit have nearly identical wavelengths .
a. Show that the wavelengths differ by
b. In the Lyman series of hydrogen, what is the wavelength difference between photons emitted in the to transition and photons emitted in the to transition?
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?
Draw a series of pictures, similar to the ground states ofand.
What is the probability of finding a hydrogen electron at distance from the proton?
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