Respuesta :
Before solving this question first we have to understand work function.
The work function of a metal is amount of minimum energy required to emit an electron from the surface barrier of metal . Whenever the metal will be exposed to radiation a part of its energy will be utilized to emit an electron while rest will provide kinetic energy to the electron.
Let f is the frequency of incident radiation and f' is the frequency corresponding to work function. Let v is the velocity of the ejected electron.
we know that velocity of an electromagnetic wave is the product of frequency and wavelength. Hence frequency f is given as-
[tex]f=\frac{c}{\lambda}[/tex]
where c is velocity of light and [tex]\lambda[/tex] is the wavelength of the wave.
As per the question incident wavelength =313 nm
[tex]313*10^{-9} m[/tex] [as 1 nm =10^-9 m]
The wavelength corresponding to work function is 351 nm i.e
[tex]351*10^{-9} m[/tex]
we know that hf=hf'+K.E [ h is the planck's constant whose value is 6.63×10^-34 J-s]
⇒K.E =hf-hf'
[tex]\frac{1}{2} mv^2=hf-hf'[/tex]
[tex]v^2=\frac{2}{m} [hf-hf'][/tex]
[tex]v^2=\frac{2}{m} [\frac{hc}{\lambda} -\frac{hc}{\lambda ' }][/tex]
[tex]=\frac{2}{9.1*10^{-31}kg } *{6.63*10^{-34} Js *3*10^{8} [\frac{1}{313*10^{-9} } -\frac{1}{351*10^{-9} } ][/tex]
[tex]=0.001512021301356*10^{14} m^2/s^2[/tex]
[tex]v=\sqrt{0.0015120241301356*10^{14} } m/s[/tex]
[tex]=0.3888476161313*10^{7} m/s[/tex]
[tex]=3.88848*10^{7} m/s[/tex] [ans]
Answer:
[tex]v = 3.94 \times 10^5 m/s[/tex]
Explanation:
As we know that the maximum wavelength needed to remove the electron from metal surface is given as
[tex]\lambda = 351 nm[/tex]
so we have work function of metal is given as
[tex]\phi = \frac{hc}{\lambda}[/tex]
[tex]\phi = \frac{1240}{351} eV[/tex]
[tex]\phi = 3.53 eV[/tex]
Now as per Einstein's equation for photo electric effect we know that
[tex]E = \phi + \frac{1}{2}mv^2[/tex]
[tex]\frac{hc}{\lambda} = \phi + \frac{1}{2}mv^2[/tex]
[tex](\frac{1240}{313} - 3.52)1.6 \times 10^{-19} = \frac{1}{2}(9.1\times 10^{-31})v^2[/tex]
[tex]7.07 \times 10^{-20} = \frac{1}{2}(9.1\times 10^{-31})v^2[/tex]
[tex]v = 3.94 \times 10^5 m/s[/tex]
