Step 1: Write the electric and magnetic energy densities.
In an electromagnetic wave, at any point:
Electric energy density: $u_E = \frac{1}{2}\varepsilon_0 E^2$
Magnetic energy density: $u_B = \frac{B^2}{2\mu_0}$
Step 2: Use the EM wave relation $E = cB$.
For an electromagnetic wave in free space, the electric and magnetic fields are always related by:
\[
E = cB \quad \text{where } c = \frac{1}{\sqrt{\mu_0\varepsilon_0}}
\]
Step 3: Substitute into the expression for electric energy density.
\[
u_E = \frac{1}{2}\varepsilon_0 E^2 = \frac{1}{2}\varepsilon_0 c^2 B^2
\]
Since $c^2 = 1/(\mu_0\varepsilon_0)$:
\[
u_E = \frac{1}{2}\varepsilon_0 \times \frac{1}{\mu_0\varepsilon_0} \times B^2 = \frac{B^2}{2\mu_0} = u_B
\]
Step 4: Interpret the result.
At every instant, the energy stored in the electric field equals the energy stored in the magnetic field. This is a fundamental property of EM waves, independent of their frequency.
Step 5: Extend to average energy densities.
Since the instantaneous values are always equal ($u_E = u_B$ at all times), their time-averaged values are also equal:
\[
K_E = \langle u_E \rangle = \langle u_B \rangle = K_B
\]
Step 6: State the answer.
\[
\boxed{K_E = K_B}
\]