= Solution
For exponential decay with <mean lifetime> $\tau$, the state amplitude evolves as $\exp[-i(E_0-i\Gamma/2)t/\hbar]$ and its survival probability is $e^{-\Gamma t/\hbar}$. Hence the energy <decay width> is
$$
\boxed{\Gamma=\frac\hbar\tau=
\frac{6.58212\times10^{-16}\ \mathrm{eV\,s}}{15\times60\ \mathrm s}
=7.31\times10^{-19}\ \mathrm{eV}.}
$$
The exceptionally small energy width expresses the long lifetime of this weak decay. Use $\hbar$, not $h$, because $\Gamma$ is an energy width in the complex-energy convention; changing to a frequency convention introduces the appropriate factor of $2\pi$. The quoted lifetime is treated as the <mean lifetime>. If a half-life were supplied instead, one would first use $\tau=t_{1/2}/\ln2$. No extra logarithm is needed for the given mean-lifetime interpretation. This calculation uses the source's approximate 15-minute value rather than silently replacing it with a more precise contemporary neutron-lifetime measurement.
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