K ₁ and K ₂ are maximum kinetic energies of photoelectrons emitted when lights of wavelength ₁ and ₂ respectively are incident on a metallic surface. If 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 wavelengths ₁ and ₂ , we have: K₁ = hc ₁ - K₂ = hc ₂ - Given ₁ = 3 ₂ , substituting this into the expression for K₁ : K₁ = hc 3 ₂ - We can express K₂ as K₂ = hc ₂ - . Multiplying by 1 3 gives: 1 3 K₂ = hc 3 ₂ - 3 Comparing K₁ and 1 3 K₂ : K₁ - 1 3 K₂ = ( hc 3 ₂ - ) - ( hc 3 ₂ - 3 ) K₁ - 1 3 K₂ = - + 3 = - 2 3 Since the work function > 0 , it follo