Question

The kinetic energy of most energetic electrons emitted from a metallic surface is doubled when the wavelength of the incident radiation is changed from $400\,nm$ to $310\,nm$ . The work function of the metal is $x\,eV$ . Find $10x$ (given $hc=1240\,eV\,nm$ )

Answer 1

Energy of photon of $400\,nm$ wavelength $=\frac{1240}{400}=3.1\,eV$
Energy of photon of $310\,nm$ wavelength $=\frac{1240}{310}=4\,eV$
$hv=\phi+k_{max}\Rightarrow 3.1=\phi+k_{max}$
$4=\phi+2k_{max}$
$\Rightarrow \phi=2.2\,eV$