The electron of a $\text{He}^{+}$ ion falls from $n = 2$ to $n = 1$ and gives out a photon. This photon is taken in by a hydrogen atom in its ground state, and the hydrogen atom loses its electron. What is the de Broglie wavelength of the electron that comes out? Use $E_n = -13.6\,\dfrac{Z^2}{n^2}\ \text{eV}$, $h = 6.626 \times 10^{-34}\ \text{J s}$, $m_e = 9.109 \times 10^{-31}\ \text{kg}$ and $1\ \text{eV} = 1.602 \times 10^{-19}\ \text{J}$.