## Question

The maximum kinetic energy of photoelectrons emitted from a certain metallic surface is 30 eV when monochromatic radiation of wavelength falls on it. When the sane surface is illuminated with light of wavelength , the maximum kinetic energy of photoelectrons is observed to be 10 eV. Calculate the wavelength and determine the maximum wavelength of incident radiation for which photoelectrons can be emitted by this surface.

### Solution

310.5 Å, 1242 Å

Let be the wavelength of the incident radiation, *W* the work function of the surface and the maximum kinetic energy of the emitted photoelectrons. Then

When illuminated with light of wavelength , then

Substituting eq. (ii) from eq. (i), we get :

.

.

= 310.5 Å.

The energy of that photon of maximum wavelength for which photoelectrons can be emitted will be equal to the work function of the surface. Thus

= 10 eV.

.

= 1242 Å.

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