Yes, the radiation efficiency of an antenna can depend on the wavelength of free space. The efficiency of an antenna refers to the ability of the antenna to convert electrical power into radiated electromagnetic energy effectively.
The radiation efficiency of an antenna is influenced by several factors, and the wavelength of the operating frequency is one of them. The efficiency tends to be higher when the size of the antenna is a significant fraction of the wavelength being used.
In general, larger antennas tend to have higher radiation efficiencies at lower frequencies. This is because a larger antenna captures a greater portion of the energy and radiates it effectively. As the frequency increases, antennas that are electrically small relative to the wavelength tend to have lower radiation efficiencies.
However, it's important to note that other factors, such as the design and construction of the antenna, the surrounding environment, and the matching between the antenna and the transmission line, can also influence the radiation efficiency. So while the wavelength is a factor, it's not the sole determinant of an antenna's radiation efficiency.