To radiate EM signal of wavelength $$\lambda$$ with high efficiency, the antennas should have a minimum size equal to:

We need to determine the minimum size of an antenna required to efficiently radiate an electromagnetic signal of wavelength $$\lambda$$.

To begin,

An antenna radiates electromagnetic waves efficiently when its physical size is comparable to the wavelength of the signal. This is because the antenna must support a standing wave pattern of current that can generate electromagnetic radiation. If the antenna is too small compared to the wavelength, it radiates very inefficiently (the radiated power drops as $$(l/\lambda)^2$$ for a short dipole).

Next,

The most basic efficient antenna is the quarter-wave monopole antenna, which has a length of $$\lambda/4$$. This is the minimum length for an antenna to be resonant at the operating frequency. At this length, the antenna forms a quarter of a standing wave, with a current maximum at the base and a current node at the tip, which is the optimal configuration for radiation.

A full half-wave dipole ($$\lambda/2$$) is the standard efficient antenna, but the minimum size for efficient radiation is $$\lambda/4$$ when a ground plane is used (which effectively mirrors the antenna, making it behave like a half-wave dipole).

From this,

The minimum antenna size for efficient radiation is $$\dfrac{\lambda}{4}$$.

The correct answer is Option 3: $$\dfrac{\lambda}{4}$$.