When photons of energies twice and thrice the work function of a metal are incident on the metal surface one after other, the maximum velocities of the photoelectrons emitted in the two cases are V₁ and V₂ respectively. The ratio V₁: V₂ is

Step-by-step solution

The maximum kinetic energy of photoelectrons follows Einstein's equation: K_ = E - W₀ , where E is the photon energy and W₀ is the work function. Kinetic energy relates to maximum velocity as K_ = 1 2 mv^2 . For E₁ = 2W₀ , the kinetic energy becomes 1 2 mV₁^2 = 2W₀ - W₀ = W₀ , yielding W₀ = 1 2 mV₁^2 . For E₂ = 3W₀ , the kinetic energy is 1 2 mV₂^2 = 3W₀ - W₀ = 2W₀ . Dividing these equations gives W₀ 2W₀ = 1 2 mV₁^2 1 2 mV₂^2 , which simplifies to V₁^2 V₂^2 = 1 2 . Taking square roots, V₁ V₂ = 1 2 . Final answer: D