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

Beginner2023-03-29Added 3 answers

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:

$M=\text{mass of electron}=9.11\times {10}^{-31}\phantom{\rule{1ex}{0ex}}\text{kg}$

$h=\text{Planck's Constant}=6.63\times {10}^{-34}\phantom{\rule{1ex}{0ex}}\text{Js}$

$c=\text{speed of light}=3\times {10}^{8}{\phantom{\rule{1ex}{0ex}}\text{ms}}^{-1}$

$\lambda =\text{wavelength of light}=206\phantom{\rule{1ex}{0ex}}\text{nm}$

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:

$M=\text{mass of electron}=9.11\times {10}^{-31}\phantom{\rule{1ex}{0ex}}\text{kg}$

$h=\text{Planck's Constant}=6.63\times {10}^{-34}\phantom{\rule{1ex}{0ex}}\text{Js}$

$c=\text{speed of light}=3\times {10}^{8}{\phantom{\rule{1ex}{0ex}}\text{ms}}^{-1}$

$\lambda =\text{wavelength of light}=206\phantom{\rule{1ex}{0ex}}\text{nm}$

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