Q.A photoelectric surface is illuminated successively by monochromatic light of wavelength $\lambda$ and $\dfrac{\lambda}{2}$. If the maximum kinetic energy of the emitted photoelectrons in the second case is 3 times that in the first case, the work function of the surface material is (NEET 2015):

Building directly on Planck's quantization idea, Einstein in 1905 proposed that light of frequency $\nu$ should itself be thought of as a stream of discrete energy quanta (photons), each carrying energy $h\nu$. Applying this to the photoelectric effect: when a single photon of energy $h\nu$ strikes a metal surface, it is completely absorbed by one single electron; part of this energy, equal to the metal's work function $\phi_0$, is spent freeing the electron from the surface, and the remainder becomes the ejected electron's kinetic energy. Conservation of energy for this one-photon-one-electron process gives Einstein's photoelectric equation, $h\nu=\phi_0+\tfrac12mv^2$; if the electron loses no energy internally on its way out, it emerges with the maximum possible kinetic energy, giving the most commonly used form $K_{max}=h\nu-\phi_0$. At the threshold frequency $\nu_0$, the photoelectron is emitted with essentially zero kinetic energy, so $h\nu_0=\phi_0$, meaning the threshold frequency is simply the photon frequency whose energy exactly equals the work function. …