In a recent experiment, physicists at UCSB were able to cool a macroscopic mecha

Question

In a recent experiment, physicists at UCSB were able to cool a macroscopic mechanical oscillator so that it was essentially in its quantum mechanical ground state with E = 0.

Assuming the frequency of the system is 9 GHz (corresponding to energy levels separated by a fixed amount e = 6 × 10-24 joules, as illustrated here), how low must the temperature have been if the probability to be out of the ground state was less than 1%?

(a) 0.06 K
(b) 0.12 K
(c) 0.29 K
(d) 0.09 K
(e) Cannot be determined from the information given.




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QUESTION 22**
If the temperature is such that the probability of having exactly one quantum of energy (i.e., E = e) is 1%, what is the probability of being in the state with E = 2e?
(a) 2%
(b) 0.5%
(c) 0.01%




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QUESTION 23**
Suppose that there were two states with E = e and one with E = 0 (i.e., the first excited level is degenerate). How would the probability P(E=0) to be in the ground state change (compared to the case of a non-degenerate first-excited level)?
(a) P(E=0) would be smaller than if the first excited level had only one state.
(b) P(E=0) would be the same as if the first excited level had only one state.
(c) P(E=0) would be greater than if the first excited level had only one state.

Explanation / Answer

The answers would be as follows: D. C. A.

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