An LC circuit is used as a transmitter to generate electromagnetic...

The frequency of the emitted electromagnetic wave is equal to the resonant frequency of the oscillating charge in the LC circuit.

The resonant frequency is given by:
$f = \dfrac{1}{2\pi \sqrt{LC}}$

Given $L = \dfrac{2.5}{\pi^2} \times 10^{-3}$ H and $C = 10^{-6}$ F, we have:
$LC = \dfrac{2.5 \times 10^{-9}}{\pi^2} = \dfrac{25 \times 10^{-10}}{\pi^2}$

$\sqrt{LC} = \dfrac{5 \times 10^{-5}}{\pi}$ s

Substituting this into the frequency formula:
$f = \dfrac{1}{2\pi \left( \dfrac{5 \times 10^{-5}}{\pi} \right)} = \dfrac{1}{10 \times 10^{-5}} = 10^4$ Hz

The wavelength $\lambda$ of the electromagnetic wave in free space is:
$\lambda = \dfrac{c}{f} = \dfrac{3 \times 10^8}{10^4} = 3 \times 10^4$ m

Answer: $3 \times 10^4$ m