When a metal surface is illuminated by light of wavelength ₁ and ₂ , the maximum velocities of photoelectrons ejected are V and 2 V respectively. The work function of the metal is ( h= Planck's constant, c= velocity of light, . ₁> ₂ )

Step-by-step solution

Photoelectric effect analysis begins with Einstein’s equation E = + K_ max , where E = hc and K_ max = 1 2 mv_ max ^2 . For wavelength ₁ with maximum velocity V : hc ₁ = + 1 2 mV^2 For wavelength ₂ with maximum velocity 2V : hc ₂ = + 2mV^2 = + 4 ( 1 2 mV^2 ) Substituting 1 2 mV^2 = hc ₁ - from the first equation: hc ₂ = + 4 ( hc ₁ - ) = 4hc ₁ - 3 Solving for : 3 = 4hc ₁ - hc ₂ = hc ( 4 ₂ - ₁ ₁ ₂ ) The work function is therefore: = hc 3 ₁ ₂ (4 ₂ - ₁) This corresponds to option D .