  We prove an uncertainty relation for energy and arrival time, where the
arrival of a particle at a detector is modeled by an absorbing term added to
the Hamiltonian. In this well-known scheme the probability for the particle's
arrival at the counter is identified with the loss of normalization for an
initial wave packet. Under the sole assumption that the absorbing term vanishes
on the initial wave function, we show that $\Delta T \Delta E \geq \sqrt p
\hbar/2$ and $<T> \Delta E\geq 1.37\sqrt p\hbar$, where $<T>e$ denotes the mean
arrival time, and $p$ is the probability for the particle to be eventually
absorbed. Nearly minimal uncertainty can be achieved in a two-level system, and
we propose a trapped ion experiment to realize this situation.
