Uncertainty Principle and the lifetime of an excited state

[CRD_98]

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?

 

[Gene Naden]

Wikipedia favors the first of your two equations where delta is the standard deviation of the quantity. Using either formula, you only get an approximate estimate. I think most instructors would accept either answer.