Question

What is the velocity of an electron that has a de Broglie wavelength approximately the length of a chemical bond? Assume this length to be 1.2 * 10-10m.

Answer 1

Answer : The velocity of an electron is, $6.1\times 10^{6}m/s$

Explanation :

According to de-Broglie, the expression for wavelength is,

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

and,

$p=mv$

where,  

p = momentum, m = mass, v = velocity

So, the formula will be:

$\lambda=\frac{h}{mv}$       .............(1)

where,

h = Planck's constant = $6.626\times 10^{-34}Js$

$\lambda$ = wavelength  = $1.2\times 10^{-10}m$

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

v = velocity of electron = ?

Now put all the given values in formula 1, we get:

$1.2\times 10^{-10}m=\frac{6.626\times 10^{-34}Js}{(9.11\times 10^{-31}kg)\times v}$

$v=6.1\times 10^{6}m/s$

Thus, the velocity of an electron is, $6.1\times 10^{6}m/s$