# Uncertainty Principle and the lifetime of an excited state

## Homework Statement

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Estimate the lifetime of the excited state of an atom whose natural emission line width is 3.00 × 10−4 eV.

## Homework Equations

$$\Delta E \Delta t = \frac{1}{2} \times \frac{h}{2\pi}$$
$$\Delta E \Delta t = \frac{h}{2\pi}$$

## The Attempt at a Solution

I think all I have to do is rearrange for Δt then sub in the energy given as ΔE, but I'm not sure when I use which equation above, the correct answer is using the second, but I thought the first equation was a more accurate improved version of the second?