Vol 2 - Landau, Lifshitz - The classical theory of fields (4th, 1994) (1) · Problem 9.1

The key is recognizing that an oscillating dipole radiates electromagnetic energy, and the power depends on how quickly the dipole moment changes. The crucial formula connects radiated power to the second time derivative of the dipole moment—essentially, the acceleration of the charge distribution. Since $p(t) = p_0 \cos(\omega t)$, its second derivative gives you $\ddot{p} \sim \omega^2 p_0$, which scales as the fourth power of frequency. Plug in the numbers using the dipole radiation formula and you'll find the answer.

The key is recognizing that an oscillating dipole radiates electromagnetic energy, and the power depends on how quickly the dipole moment changes. The crucial formula connects radiated power to the second time derivative of the dipole moment—essentially, the acceleration of the charge distribution. Since $p(t) = p_0 \cos(\omega t)$, its second derivative gives you $\ddot{p} \sim \omega^2 p_0$, which scales as the fourth power of frequency. Plug in the numbers using the dipole radiation formula and you'll find the answer.