What is the De Broglie wavelength of an electron given it has a kinetic energy of 1 eV? You are given the mass of an electron is 9.11x10^-31 kg and Planck's constant is 6.63x10^-34

The De Broglie wavelength equation is as follows:

λ=h/p

We know the value of Planck's constant h and so to calculate the wavelength all we need is the momentum, which is equal to mv.

The kinetic energy is given as 1 eV. Remember 1 eV is equal to 1.6 x 10^-19 Joules. Using the equation for kinetic energy and the given mass of the electron we can determine the velocity of the electron as follows:

K.E = 0.5mv²

Which can be rearranged to be in terms of velocity v:

v = (2K.Em)^0.5

By substituting in 1.6 x 10^-19 for K.E and 9.11 x 10^-31 for m we get v = 5.93 x 10⁵ ms^-1 (remember to keep the full non-rounded value in your calculator!)

Then using the initial equation for the wavelength and remembering p = mv, we can substitute in our values for h, m and v as follows:

λ = 6.33 x 10^-34 / (9.11 x 10^-31 x 5.93 x 10⁵)  

λ = 1.17 x 10^-9 m