Respuesta :
Answer:
The velocity of an ejected electron when the student employed light with a wavelength of 313 nm is [tex]3.385\times 10^{5} m/s[/tex].
Explanation:
The mathematical equation for studying the photoelectric effect is:
[tex]h\nu = W + \frac{1}{2} m_e\times \mu ^2[/tex]
We have :
Wavelength of light which can dislodge electrons from a metal surface = [tex]\lambda =341 nm=341\times 10^{-9} m[/tex]
[tex]1 nm=10^{-9} m[/tex]
Energy needed to remove an electron from the metal :
[tex]W=\frac{hc}{\lambda }[/tex] (Planck's equation)
[tex]=\frac{6.626\times 10^{-34} Js\times 3\times 10^8 m/s}{341\times 10^{-9} m}=5.829\times 10^{-19} J[/tex]
Frequency of light shinning on metal surface = [tex]\nu =?[/tex]
Wavelength of light shinning on metal surface = [tex]\lambda '=313 nm=313\times 10^{-9} m[/tex]
[tex]nu=\frac{c}{\lambda '}=\frac{3\times 10^8 m/s}{313\times 10^{-9} m}=9.585 \times 10^{14}Hz[/tex]
Mass of electron = [tex]m_e=9.109\times 10^{-31} kg[/tex]
Velocity of electron = u
[tex]6.626\times 10^{-34} J.s\times 9.585\times 10^{14} Hz=5.829\times 10^{-19} J+\frac{1}{2}\times 9.109\times 10^{-31} kg\times (u)^2[/tex]
[tex]u = 3.385\times 10^{5} m/s[/tex]
The velocity of an ejected electron when the student employed light with a wavelength of 313 nm is [tex]3.385\times 10^{5} m/s[/tex].
