Question

An electron has kinetic energy 3.00 ev. find its wavelength.

Answer 1

First we need to convert the electron's energy in Joule. Keeping in mind that

`1 eV = 1.6 \cdot 10^(-19) J`
3 eV corresponds to

`K=3 eV = 3 \cdot 1.6 \cdot 10^(-19)J=4.8 \cdot 10^(-19) J`

The kinetic energy of an electron is related to its momentum by the formula

`K= (p^2)/(2m)`
where p is the electron's momentum, while m is its mass. Re-arranging the formula, we find

`p= √(2Km)= \sqrt{2 (4.8 \cdot 10^(-19)J)(9.1 \cdot 10^(-31) kg)}=9.35 \cdot 10^(-25) kg m/s`

And then we can use De Broglie relationship to find its wavelength:

`\lambda= (h)/(p)= (6.6 \cdot 10^(-34)Js)/(9.35 \cdot 10^(-25) kg m/s)=7.06 \cdot 10^(-10) m`