When light of frequency 1.5 10¹⁵ Hz illuminates a metal surface, the maximum kinetic energy of the emitted photoelectrons is 2.07 eV. Which of the following incident wavelengths will not cause photoelectric emission from this metal? (Take h = 4.14 10⁻¹⁵ eV s and c = 3 10^8 m/s)

Step-by-step solution

First, calculate the energy of the incident photons for the initial light source: E = h E = (4.14 10⁻¹⁵ eV s ) (1.5 10¹⁵ Hz ) = 6.21 eV Using Einstein's photoelectric equation, find the work function ( ) of the metal: K_ max = E - = E - K_ max = 6.21 eV - 2.07 eV = 4.14 eV Next, determine the threshold wavelength ( ₀ ) for this metal: ₀ = hc ₀ = 4.14 10⁻¹⁵ 3 10^8 4.14 m ₀ = 3 10⁻⁷ m = 300 nm For photoelectric emission to take place, the incident wavelength must be less than or equal to the threshold wavelength ( ₀