Question

Violet light of wavelength 427 nm ejects electrons with a maximum kinetic energy of 0.684 eV from a certain metal. What is the work function of this metal (in eV)?

Answer 1

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;

$E = hf = \frac{hc}{\lambda} = \frac{6.626 \ \times \ 10^{-34} \ \times\ 3\ \times \ 10^8 }{427 \ \times \ 10^{-9}} = 4.655 \ \times \ 10^{-19} \ J\\\\1 \ eV = 1.6 \ \times \ 10^{-19} \ J\\\\E =( \frac{4.655 \ \times \ 10^{-19} \ J }{1.6 \ \times \ 10^{-19} \ J} ) \ eV\\\\E = 2.91 \ eV$

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.