(Solved): The surface Brillouin zones of several surface reconstructions on \( \mathrm{Si}(111) \) have the ...

The surface Brillouin zones of several surface reconstructions on \( \mathrm{Si}(111) \) have the following relations (see the drawing). Si has a lattice of \( 5.431 \AA \). (a) Calculate the size of the wave vector \( \overline{M M} \) for a \( 7 \times 7 \) surface Brillouin zone.