If K₁ and K₂ are maximum kinetic energies of photoelectrons emitted when lights of wavelengths ₁ and ₂ , respectively incident on a metallic surface and ₁=3 ₂ , then

Step-by-step solution

According to Einstein's photoelectric equation, the maximum kinetic energy K of emitted photoelectrons is given by K = hc - , where is the work function of the metal. For the first wavelength ₁ , K₁ = hc ₁ - . For the second wavelength ₂ , K₂ = hc ₂ - . Given ₁ = 3 ₂ , we substitute this into the expression for K₁ : K₁ = hc 3 ₂ - = 1 3 ( hc ₂ - 3 ) . Since K₂ = hc ₂ - , we have hc ₂ = K₂ + . Substituting this into the expression for K₁ : K₁ = 1 3 (K₂ + - 3 ) = K₂ - 2 3 = K₂ 3 - 2 3 . Since > 0 , it follows that K₁