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a) In nano-mechanical force spectroscopy on a given sample a rectangular cantilever beam made of S13N4 was used. The length, width and thickness of the cantilever was 100 m, 20 um and 0.6 um, respectively. Calculatea) the vertical spring constant (kz) of the cantileverandb) the resonance frequency of the cantilever?Assume that the modulus of rigidity of Si3N4 is 150 GPa and its density is 3170 kg-m-3 b) Explain in three sentences, why does one can only see half of the atoms on scanning tunnelling microscopy images of graphite. c) List three scanning probe techniques and explain which respective interactions are studied in these techniques.