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## Q. 10.3

Why do we say that $\Delta t=\hbar /(2 \Delta E)$ is a lower-bound estimate of the lifetime of an atomic state? Why isn’t that the exact or approximate value of the lifetime?

## Verified Solution

The width of the spectral line ΔE presumably comes from a series of measurements, each having some inherent uncertainty, plus some deviation due to a lack of experimental precision. Therefore we can expect that a measured ΔE will usually be larger than the minimum allowed by the Heisenberg uncertainty principle. A larger value of ΔE leads to a smaller Δt, because of the inverse nature of the relationship, and the true value of Δt will be larger.