Question

5. (10 pts) (a) Einstein's explanation of the photoelectric effect launched the study of quantum mechanics. A minimum frequency of UV light shining on a metal is necessary to create a current. Explain in your own words, how Einstein explained this particular observation. Be to the point. Points will be deducted for answers that do not have enough detail, or if there is irrelevant information. (b) You discover a new metal. You conduct a photoelectric experiment on the metal using light of wavelength 253.5 nm and find that the stopping potential is V. What is the work function of the metal?

Thanks!

Answer 1

a)

A minimum frequency of UV light shining on a metal is necessary to create a current. Einstein explained this observation in the following manner.

A current can be created if free electrons are available. Each of the electron of an atom is bound to the nucleus due to Coulombian attractive force. Energy needed to be spent in order to release the electron from an atom and this can be achieved by supplying required quantity of energy in the form of UV light. The minimum energy needs to release electrons from a metal surface is called photoelectric work function. The energy of a radiation is determined by its frequency.

b)

wavelength of incident light, λ = 253.5 nm = 253.5 x 10-9 m

energy of incident light, E = hc/λ = 6.625 x 10-34 x 3 x 108 /253.5 x 10-9 m = 7.84 x 10-19 J

the stopping potential = V

kinetic energy of photoelectrons, K = eV where e is the charge of electron.

Using Einstein’s photoelectric equation,

E = W + K where W is the work function

Work function, W = E – K = E – eV = (7.84 x 10-19 – 1.6 x 10-19 V) J

Work function, W = (7.84 x 10-19 – 1.6 x 10-19 V) J