Physicists use laser beams to create an atom trap in which

Chapter 39, Problem 39.66

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Physicists use laser beams to create an atom trap in which atoms are confined within a spherical region of space with a diameter of about 1 mm. The scientists have been able to cool the atoms in an atom trap to a temperature of approximately 1 nK, which is extremely close to absolute zero, but it would be interesting to know if this temperature is close to any limit set by quantum physics. We can explore this issue with a onedimensional model of a sodium atom in a 1.0-mm-long box. a. Estimate the smallest range of speeds you might find for a sodium atom in this box. b. Even if we do our best to bring a group of sodium atoms to rest, individual atoms will have speeds within the range you found in part a. Because theres a distribution of speeds, suppose we estimate that the root-mean-square speed vrms of the atoms in the trap is half the value you found in part a. Use this vrms to estimate the temperature of the atoms when theyve been cooled to the limit set by the uncertainty principle