With reference to the observations in photo-electric effect,...

From Einstein's photoelectric equation, 

Maximum kinetic energy, K{E}_\max = \dfrac{1}{2}m{v}_\max^{2} = hf - ϕ, where, {v}_\max is maximum velocity of photoelectrons, $h$ is Planck's constant, $f$ is frequency of incident light and $ϕ$ is work function of metal.

From above relation, we can see that the square of maximum velocity of photoelectrons varies linearly with frequency of incident light.

If we increase the intensity of the incident radiation by keeping the frequency constant, then the value of saturation current increases in proportion to the intensity of the incident radiation. Thus, saturation current decreases on moving the source of light away from the metal surface.

The kinetic energy of the photoelectrons is directly proportional to the light frequency, and it remains constant as light amplitude or power of source increases.

Photoelectric effect cannot be explained on the basis of wave nature because experimentally a particular energy called the work function of the metal surface in needed to eject electrons from surface, irrespective of the time for which light is incident. 

Photoelectric effect can be explained by particle nature of light (i.e. quantum theory). Threshold wavelength is maximum wavelength at which emission takes place.