Answer
The maximum length of the antenna is $3.0~cm$
Work Step by Step
We can find the wavelength of the microwaves:
$\lambda = \frac{c}{f}$
$\lambda = \frac{3.0\times 10^8~m/s}{5.0\times 10^9~Hz}$
$\lambda = 0.060~m = 6.0~cm$
Since the antenna is not to exceed half of a wavelength, the maximum length of the antenna is $3.0~cm$
