Answer: The electron moves slower than the speed of light
Explanation:
The de Broglie wavelength [tex]\lambda[/tex] is given by the following formula:
[tex]\lambda=\frac{h}{p}[/tex] (1)
Where:
[tex]h=6.626(10)^{-34}\frac{m^{2}kg}{s}[/tex] is the Planck constant
[tex]p[/tex] is the momentum of the atom, which is given by:
[tex]p=m_{e}v[/tex] (2)
Where:
[tex]m_{e}=9.11(10)^{-28}g=9.11(10)^{-31}kg[/tex] is the mass of the electron
[tex]v[/tex] is the velocity of the electron (the value we want to find)
Substituting (2) in (1):
[tex]\lambda=\frac{h}{m_{e}v}[/tex] (3)
Finding [tex]v[/tex] :
[tex]v=\frac{h}{m_{e}\lambda}[/tex] (4)
[tex]v=\frac{6.626(10)^{-34}\frac{m^{2}kg}{s}}{(9.11(10)^{-31}kg)(3.31(10)^{-10}m/s)}[/tex] (5)
Finally:
[tex]v=2.197(10)^{6} m/s[/tex]>>> This is the velocity of the electron, which compared to the [tex]v=3(10)^{8} m/s[/tex] of the light is quite slower.
