Light of wavelength 575nm is directed at a metallic surface with a work function of 1.60eV.
(a) if the maximum kinetic energy is 9.0 *10^-20J, what is the maximum speed of this electron?( m= 9.11*10^-31kg)
First, we need to use the formula for the maximum kinetic energy of an electron emitted from a metal surface due to the photoelectric effect:
Kmax = hf - φ
where Kmax is the maximum kinetic energy of the electron, h is Planck's constant (6.626 x 10^-34 J*s), f is the frequency of the incident light (which we can calculate from the wavelength using c = λf, where c is the speed of light), and φ is the work function of the metal surface.
Let's start by finding the frequency of the light:
c = λf
f = c/λ
f = (3.00 x 10^8 m/s)/(575 x 10^-9 m)
f = 5.22 x 10^14 Hz
Now we can calculate the maximum kinetic energy:
Kmax = hf - φ
Kmax = (6.626 x 10^-34 J*s)(5.22 x 10^14 Hz) - 1.60 eV
Kmax = 3.46 x 10^-19 J - 1.60 x 1.6 x 10^-19 J
Kmax = 1.83 x 10^-19 J
Finally, we can use the formula for kinetic energy to find the maximum speed of the electron:
Kmax = 1/2 mv^2
v = √(2Kmax/m)
v = √(2(1.83 x 10^-19 J)/(9.11 x 10^-31 kg))
v = 5.45 x 10^5 m/s
So the maximum speed of the electron is 5.45 x 10^5 m/s.