An atomic force microscope (AFM) calibration experiment is conducted to measure the vertical deflection δ\deltaδ of a micro-fabricated silicon cantilever when a micro-mass mmm is deposited on its free end. The relation between the deflection and the mass is given by:
δ=ΓmE \delta = \frac{\Gamma m}{E} δ=EΓmwhere EEE is the Young modulus of the cantilever material and Γ\GammaΓ is a calibration constant.
A graph of the cantilever's vertical deflection δ\deltaδ (in μm\mu\text{m}μm) against the deposited mass mmm (in μg\mu\text{g}μg) yields a straight line passing through the origin. From the line of best fit, a mass of m=2.5 μgm = 2.5\ \mu\text{g}m=2.5 μg corresponds to a vertical deflection of δ=0.35 μm\delta = 0.35\ \mu\text{m}δ=0.35 μm.
Given that the Young modulus of the silicon cantilever is E=120 GPaE = 120\text{ GPa}E=120 GPa, determine the order of magnitude of Γ\GammaΓ in s−2\text{s}^{-2}s−2.