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Chapter 41: Q. 24 (page 1207)
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?
a. The wavelength is .
b. The power output of this laser is.
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A helium-neon laser emits a visible laser beam with a wavelength of . How many photons are emitted per second?
The Nobel Prize in physics went to Steven Chu, Claude Cohen-Tannoudji, and William Phillips for their development of techniques to slow, stop, and 鈥渢rap鈥� atoms with laser light. To see how this works, consider a beam of rubidium atoms traveling at after being evaporated out of an oven. A laser beam with a wavelength of is directed against the atoms. This is the wavelength of the transition in rubidium, with being the ground state, so the photons in the laser beam are easily absorbed by the atoms. After an average time of , an excited atom spontaneously emits a wavelength photon and returns to the ground state.
a. The energy-momentum-mass relationship of Einstein鈥檚 theory of relativity is . A photon is massless, so the momentum of a photon is . Assume that the atoms are traveling in the positive x-direction and the laser beam in the negative x-direction. What is the initial momentum of an atom leaving the oven? What is the momentum of a photon of light?
b.The total momentum of the atom and the photon must be conserved in the absorption processes. As a consequence, how many photons must be absorbed to bring the atom to a halt?
NOTE Momentum is also conserved in the emission processes. However, spontaneously emitted photons are emitted in random directions. Averaged over many absorption/emission cycles, the net recoil of the atom due to emission is zero and can be ignored.
c. Assume that the laser beam is so intense that a ground-state atom absorbs a photon instantly. How much time is required to stop the atoms?
d. Use Newton鈥檚 second law in the form to calculate the force exerted on the atoms by the photons. From this, calculate the atoms鈥� acceleration as they slow.
e. Over what distance is the beam of atoms brought to a halt?
Draw a series of pictures, similar to the ground states of , and .
Show that .
atoms are excited to an upper energy level at . At the end of , of these atoms have undergone a quantum jump to the ground state.
a. How many photons have been emitted?
b. What is the lifetime of the excited state?
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