Paloma Houston

2023-03-28

A clean nickel surface (work function 5.1eV), is exposed to light of wavelength 206nm. What is the maximum speed of the photoelectrons emitted from this surface?

moodleacnn

An electron of the metal can receive photon energy from incident light, which is equal to the planck's constant times the light's frequency.
Since wavelength is given here, frequency = velocity of light/wavelength.
The photoelectric equation mentioned above can be used to determine the photoelectrons' top speed.
Under the assumption that the whole photon energy is used up
First -in taking out electron from the metal (work function)
Secondly -the left over is provided as the kinetic energy to the photo-electron
When one puts in the numbers ,the maximum speed can be of the order of ${10}^{5}\frac{\text{meters}}{\text{s}}$.
$V\left(m\right)=\sqrt{\frac{2}{M}\left(\frac{hc}{\lambda }\right)-5.1\text{eV}}$
where:
$M=\text{mass of electron}=9.11×{10}^{-31}\phantom{\rule{1ex}{0ex}}\text{kg}$
$h=\text{Planck's Constant}=6.63×{10}^{-34}\phantom{\rule{1ex}{0ex}}\text{Js}$
$c=\text{speed of light}=3×{10}^{8}{\phantom{\rule{1ex}{0ex}}\text{ms}}^{-1}$
$\lambda =\text{wavelength of light}=206\phantom{\rule{1ex}{0ex}}\text{nm}$

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