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
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