a) The minimum frequency of the light must be [tex]1.26\cdot 10^{15} Hz[/tex]
b) The maximum velocity of the electrons is [tex]5.93\cdot 10^5 m/s[/tex]
Explanation:
a)
The photoelectric effect is a phenomenon that occurs when electromagnetic radiation hits the surface of a metal causing the release of electrons from the metal's surface.
The equation of the photoelectric effect is:
[tex]hf = \phi +K_{max}[/tex]
where :
[tex]hf[/tex] is the energy of the incoming photons, where
[tex]h[/tex] is the Planck's constant
[tex]f[/tex] is the frequency of the incoming photons
[tex]\phi[/tex] is the work function of the metal, the minimum energy that the photons must have in order to be able to free electrons from the metal
[tex]K_{max}[/tex] is the maximum kinetic energy of the emitted electrons
In order to free electrons, the minimum energy of the photons must be at least  equal to the work function (so that the kinetic energy of the electrons is zero, [tex]K_{max}=0[/tex]. Therefore,
[tex]h f_0 = \phi[/tex]
In this case,
[tex]\phi = 5.22 eV \cdot (1.6\cdot 10^{-19})=8.35\cdot 10^{-19} J[/tex]
Therefore, the minimum frequency of the photons must be
[tex]f_0 = \frac{\phi}{h}=\frac{8.35\cdot 10^{-19}}{6.63\cdot 10^{-34}}=1.26\cdot 10^{15} Hz[/tex]
b)
In this case, the wavelength of the incoming light is
[tex]\lambda = 200 nm = 200 \cdot 10^{-9} m[/tex]
We can find the frequency by using the wave equation:
[tex]f=\frac{c}{\lambda}=\frac{3\cdot 10^8}{200\cdot 10^{-9}}=1.5\cdot 10^{15} Hz[/tex]
Now we can use the equation of the photoelectric effect to find the maximum kinetic energy of the electrons:
[tex]K_{max} = hf-\phi = (6.63\cdot 10^{-34})(1.5\cdot 10^{15})-8.35\cdot 10^{-19}=1.60\cdot 10^{-19} J[/tex]
And therefore, we can find their velocity by using the equation for the kinetic energy:
[tex]K_{max} = \frac{1}{2}mv^2[/tex]
where
[tex]m=9.11\cdot 10^{-31} kg[/tex] is the mass of the electrons
v is their speed
Solving for v,
[tex]v=\sqrt{\frac{2K_{max}}{m}}=\sqrt{\frac{2(1.6\cdot 10^{-19})}{9.11\cdot 10^{-31}}}=5.93\cdot 10^5 m/s[/tex]
Learn more about photoelectric effect:
brainly.com/question/10015690
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