Lights of wavelengths λ 1 = 340 nm and λ 2 = 540 nm are incident on a metallic surface. If the ratio of the maximum speeds of the electrons ejected is 2 , the work function of the metal is

Step-by-step solution

λ 1 = 350   nm ,   λ 2 = 540   nm ,    V 1 V 2 = 2 ⇒ V 1 = 2 V   and   V 2 = V hc λ 1 = ϕ + 1 2 m ( 2 V ) 2 hc λ 2 = ϕ + 1 2 mV 2 hc λ 1 - hc λ 2 × 4 = ϕ - 4 ϕ hc ( 4 540   nm - 1 340   nm ) = 3 ϕ ϕ = 1.8  eV