Answer
$w = 4.88~mm$
Work Step by Step
We can find width of the central maximum:
$w = \frac{2.44~\lambda~L}{d}$
$w = \frac{(2.44)~(500\times 10^{-9}~m)(2.0~m)}{0.50\times 10^{-3}~m}$
$w = 4.88\times 10^{-3}~m$
$w = 4.88~mm$
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