Question

What is the speed of an electron that has a de Broglie wavelength of 100. nm?

Answer 1

Answer: The speed of the electron is $7.24\times 10^3m/s$

Explanation:

To calculate the speed of electron for given wavelength, we use the equation given by De-Broglie's, which is:

$\lambda=\frac{h}{mv}$

where,

$\lambda$ = De-Broglie's wavelength = $100nm=100\times 10^{-9}m$

h = Planck's constant = $6.6\times 10^{-34}Js$

m = mass of the electron = $9.11\times 10^{-31}kg$

v = speed of the electron = ?

Putting values in above equation, we get:

$100\times 10^{-9}m=\frac{6.6\times 10^{-34}Js}{9.11\times 10^{-31}kg\times v}\\\\v=\frac{6.6\times 10^{-34}Js}{9.11\times 10^{-31}kg\times 100\times 10^{-9}m}=7.24\times 10^3m/s$

Hence, the speed of the electron is $7.24\times 10^3m/s$