Question

The work function for a metal surface is 3.82 eV. What is the largest wavelength of light in nm that will produce photoelectrons from this surface?1 eV = 1.602 ? 10?19 J,

e = 1.602 ? 10?19 C,
c = 2.998 ? 108 m/s,
and
h = 6.626 ? 10?34 J

Answer 1

The largest wavelength of light that will produce photoelectrons from this surface is 324.6 nm.

Step-by-step explanation:

Given;

work function, Ф = 3.82 eV

The work function of the metal is minimum energy required to produce electron from the metal surface.

Ф = hf

where;

h is Planck's constant = 6.626 x 10⁻³⁴ J/s

f is the frequency of the photon

f = c / λ

`\phi = (hc)/(\lambda)`

where;

c is speed of light = 2.998 x 10⁸ m/s

λ is the wavelength = ?

`\phi = (hc)/(\lambda)\\\\\lambda = (hc)/(\phi )\\\\\lambda = ((6.626*10^(-34))(2.998*10^8))/(3.82*1.602*10^(-19))\\\\\lambda = 3.246*10^(-7) \ m\\\\\lambda = 324.6 *10^(-9) \ m\\\\\lambda = 324.6 \ nm`

Therefore, the largest wavelength of light that will produce photoelectrons from this surface is 324.6 nm.