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

The work function of the metal is 2.226 eV.

Step-by-step 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 = (hc)/(\lambda) = (6.626 \ * \ 10^(-34) \ *\ 3\ * \ 10^8 )/(427 \ * \ 10^(-9)) = 4.655 \ * \ 10^(-19) \ J\\\\1 \ eV = 1.6 \ * \ 10^(-19) \ J\\\\E =( (4.655 \ * \ 10^(-19) \ J )/(1.6 \ * \ 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.