Monochromatic light of wavelength is incident on a metal surface whose work function is equal to hc 3 . The de Broglie wavelength of the fastest emitted photoelectrons is (where m is the mass of an electron, c is the speed of light in vacuum, and h is Planck's constant):

Step-by-step solution

From Einstein's photoelectric equation, the maximum kinetic energy K_ of the emitted photoelectrons is: K_ = hc - Given the work function = hc 3 , we have: K_ = hc - hc 3 = 2hc 3 The de Broglie wavelength _d of an electron with kinetic energy K is given by: _d = h 2mK_ Substituting the value of K_ : _d = h 2m ( 2hc 3 ) _d = h 4mhc 3 Bringing h inside the square root as h^2 : _d = 3 h^2 4mhc = 3h 4mc Using the work function as the kinetic energy leads to 3h 2mc , and using the incident energy leads to h 2mc . Answer