Question

A graph is shown between the maximum kinetic energy (\( E_k \)) of emitted photoelectrons and frequency (\( \nu \)) of the incident light in an experiment of the photoelectric effect. Find:
(i) Threshold frequency
(ii) Work function (in eV)
(iii) Planck's constant 

Hint:

For photoelectric effect problems, use the equation \( E_k = h (\nu - \nu_0) \) and determine values from the graph.

Answer 1

From the graph: The threshold frequency (\( \nu_0 \)) is the x-intercept of the graph: \[ \nu_0 = 2.5 \times 10^{14} \, \mathrm{Hz}. \] The work function (\( \phi \)) is given by: \[ \phi = h \nu_0 = (6.6 \times 10^{-34}) (2.5 \times 10^{14}) = 1.65 \times 10^{-19} \, \mathrm{J}. \] Converting to eV: \[ \phi = \frac{1.65 \times 10^{-19}}{1.6 \times 10^{-19}} = 1 \, \mathrm{eV}. \] \item From the slope of the graph, Planck's constant \( h \) is: \[ h = \frac{\Delta E_k}{\Delta \nu} = \frac{5 \times 10^{-19}}{7 \times 10^{14} - 2.5 \times 10^{14}} = 6.6 \times 10^{-34} \, \mathrm{Js}. \]