Matter and waves

Exercise 4

$m_{électron}$ $=$ $9.11\cdot 10^{-31}kg$; $1eV$ $=$ $1.6\cdot 10^{-19}J$. What is the wavelength of an electron with a kinetic energy of $13.6\;eV$

$\frac{mv^2}{2}$ $=$ $13.6\cdot 1.6\cdot 10^{-19}$ $ m^2v^2$ $=$ $2\cdot 13.6\cdot 1.6\cdot 10^{-19}\cdot 9.11\cdot 10^{-31}$ $mv$ $=$ $\sqrt{2\cdot 13.6\cdot 1.6\cdot 10^{-19}\cdot 9.11\cdot 10^{-31}}$ $\lambda$ $=$ $\frac{h}{mv}$=$\frac{6.626\cdot 10^{-34}}{\sqrt{2\cdot 13.6\cdot 1.6\cdot 10^{-19}\cdot 9.11\cdot 10^{-31}}}$= $3.32\cdot 10^{-10}m$