Answer:
The work function of the metal is 2.226 eV.
Explanation:
Given;
wavelength of the violet light, λ = 427 nm = 427 x 10⁻⁹ m
maximum kinetic energy, K.E = 0.684 eV
The energy of the incident light is calculated as;
[tex]E = hf = \frac{hc}{\lambda} = \frac{6.626 \ \times \ 10^{-34} \ \times\ 3\ \times \ 10^8 }{427 \ \times \ 10^{-9}} = 4.655 \ \times \ 10^{-19} \ J\\\\1 \ eV = 1.6 \ \times \ 10^{-19} \ J\\\\E =( \frac{4.655 \ \times \ 10^{-19} \ J }{1.6 \ \times \ 10^{-19} \ J} ) \ eV\\\\E = 2.91 \ eV[/tex]
Apply Einstein's photoelectric equation;
E = Ф + K.E
where;
Ф is the work function of the metal
Ф = E - K.E
Ф = 2.91 eV - 0.684 eV
Ф = 2.226 eV.
Therefore, the work function of the metal is 2.226 eV.
