Light of frequency 3 ₀ is incident on a metal surface having a threshold frequency ₀ . If m is the mass of an electron and h is Planck's constant, the de Broglie wavelength of the emitted photoelectron with the maximum kinetic energy is:

Step-by-step solution

First, we find the maximum kinetic energy ( K_ max ) of the emitted photoelectrons using Einstein's photoelectric equation: K_ max = h - h ₀ Given the incident frequency = 3 ₀ , we get: K_ max = h(3 ₀) - h ₀ = 2h ₀ The de Broglie wavelength of an electron with kinetic energy K_ max is given by: = h 2mK_ max Substituting the value of K_ max : = h 2m(2h ₀) = h 4mh ₀ Answer: h 4mh ₀