Problem 6.248

What is the minimum height to which a gamma quanta source containing excited \(\mathrm{Zn}^{67}\) nuclei has to be raised for the gravitational displacement of the Mössbauer line to exceed the line width itself, when registered on the Earth's surface? The registered gamma quanta are known to have an energy \(\varepsilon=93 \mathrm{keV}\) and appear on transition of \(\mathrm{Zn}^{67}\) nuclei to the ground state, and the mean lifetime of the excited state is \(\tau=14 \mu \mathrm{s}\)