Answer: The speed of the electron is [tex]7.24\times 10^3m/s[/tex]
Explanation:
To calculate the speed of electron for given wavelength, we use the equation given by De-Broglie's, which is:
[tex]\lambda=\frac{h}{mv}[/tex]
where,
[tex]\lambda[/tex] = De-Broglie's wavelength = [tex]100nm=100\times 10^{-9}m[/tex]
h = Planck's constant = [tex]6.6\times 10^{-34}Js[/tex]
m = mass of the electron = [tex]9.11\times 10^{-31}kg[/tex]
v = speed of the electron = ?
Putting values in above equation, we get:
[tex]100\times 10^{-9}m=\frac{6.6\times 10^{-34}Js}{9.11\times 10^{-31}kg\times v}\\\\v=\frac{6.6\times 10^{-34}Js}{9.11\times 10^{-31}kg\times 100\times 10^{-9}m}=7.24\times 10^3m/s[/tex]
Hence, the speed of the electron is [tex]7.24\times 10^3m/s[/tex]
