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What is the minimum height to which a gamma quanta source containing excited Zn^(67) nuclei has to be raised for the gravitational displacement of the Mossbauer line to exceed the line width itself, when registered on the Earth's surface? The registered gamma quanta are known to have an energy epsilon= 93keV and appear on transition of Zn^(67) nuclei to the ground state, and the mean lifetime of the exited state is tau=14 mu s. |
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Answer» Solution :The natural LIFE time is `GAMMA=( ħ)/(tau)= 4.7xx10^(-10)eV` Thus the condition `deltaE_(gamma)GE Gamma" implies" (gh)/(c^(2))ge(Gamma)/(epsilon)=( ħ)/(tau epsilon)` or `h ge(c^(2) ħ)/(tau epsilong)= 4.64` meter. ( `h` here is height of the place, not plank's constant.) |
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