When a metallic surface is illuminated with radiation of frequency , the maximum velocity of the emitted photoelectrons is v . When the frequency of the incident radiation is increased to 3 , the maximum velocity of the photoelectrons becomes 2v . The threshold frequency of the metal is:

Step-by-step solution

According to Einstein's photoelectric equation, the maximum kinetic energy is given by: K_ = h - h ₀ For the first case, the maximum velocity is v : 1 2 mv^2 = h - h ₀ (1) For the second case, the frequency is 3 and the maximum velocity is 2v : 1 2 m(2v)^2 = h(3 ) - h ₀ 4 ( 1 2 mv^2 ) = 3h - h ₀ (2) Substituting equation (1) into equation (2): 4(h - h ₀) = 3h - h ₀ 4h - 4h ₀ = 3h - h ₀ h = 3h ₀ ₀ = 3 Thus, the threshold frequency is 3 . Answer: 3