The work functions of Aluminium and Gold are 4 . 1 eV and 5 . 1 eV respectively. The ratio of the slope of the stopping potential versus frequency plot for Gold to that of Aluminium is

Step-by-step solution

The data given is ϕ A l = 4 . 1   eV ϕ A u = 5 . 1   eV The energy is given by h ν = ϕ + K E ⇒ h ν = ϕ + e V 0 where V 0 is the stopping potential and K = e V 0 Thus, the above equation can be written as e V 0 = h ν - ϕ ⇒ V 0 = h ν e - ϕ e The equation is of the form of y = m x + c . The slope is m = h e . Since the Planck constant h and charge of an electron is a constant e , the slope does not depend on the work function. Hence the ratio of t