  We prove the uncertainty relation $\sigma_T \, \sigma_E \geq \hbar/2$ between
the time $T$ of detection of a quantum particle on the surface $\partial
\Omega$ of a region $\Omega\subset \mathbb{R}^3$ containing the particle's
initial wave function, using the "absorbing boundary rule" for detection time,
and the energy $E$ of the initial wave function. Here, $\sigma$ denotes the
standard deviation of the probability distribution associated with a quantum
observable and a wave function. Since $T$ is associated with a POVM rather than
a self-adjoint operator, the relation is not an instance of the standard
version of the uncertainty relation due to Robertson and Schr\"odinger. We also
prove that if there is nonzero probability that the particle never reaches
$\partial \Omega$ (in which case we write $T=\infty$), and if $\sigma_T$
denotes the standard deviation conditional on the event $T<\infty$, then
$\sigma_T \, \sigma_E \geq (\hbar/2) \sqrt{\mathrm{Prob}(T<\infty)}$.
