In the photoelectric effect, electrons are ejected from a metal surface when light strikes it. A certain minim

Question

In the photoelectric effect, electrons are ejected from a metal surface when light strikes it. A certain minimum energy, Emin, is required to eject an electron. Any energy absorbed beyond that minimum gives kinetic energy to the electron. It is found that when light at a wavelength of 540nm falls on a cesium surface, an electron is ejected with a kinetic energy of 2.60x10^-20 J. When the wavelength is 400 nm, the kinetic energy is 1.54x10^-19 J.

A. calculate the Emin for cesium in joules.

B. calculate the longest wavelength, in nanometers, that will eject electrons from cesium.

Answer 1

The energy of a photon is:

E = hc / λ

The energy of a photon with 540nm wavelength is therefore:

E = 6.626068*10^-34 * 299792458 / (540*10^-9)

E = 3.6786*10^-19 J

Since the kinetic energy of the electron is known:

Emin = 3.6786*10^-19 - 2.60*10^-20

Emin = 3.4186*10^-19

Emin = 3.42*10^-19 J

The longest wavelength of light that will cause an ejection of an electron has an energy equal to that of Emin:

Emin = hc / λ

3.42*10^-19 = 6.626068*10^-34 * 299792458 / λ

λ = 5.81*10^-7 m

λ = 581 nm