/sci/ - Science & Math

(Fig. 14.50 of 3rd ed., Knight, Physics for Scientists and Engineers). It has recently become possible to "weigh" DNA molecules by measuring the influence of their mass on a nano-oscillator. Fig. 14.50 shows a thin rectangular cantilever etched out of silicon (density 2300 kg/m3) with a small gold dot at the end. If pulled down and released, the end of the cantilever vibrates with simple harmonic motion, moving up and down like a diving board after a jump. When bathed with DNA molecules whose ends have been modified to bind with gold, one or more molecules may attach to the gold dot. The addition of their mass causes a very slight--but measurable--decrease in the oscillation frequency. A vibrating cantilever of mass M can be modeled as a block of mass 1/3 M attached to a spring. (The factor of 1/3 arises from the moment of inertia of a bar pivoted at one end.) Neither the mass nor the spring constant can be determined very accurately--perhaps to only two significant figures--but the oscillation frequency can be measured with very high precision simply by counting the oscillations. In one experiment, the cantilever was initially vibrating at exactly 18 MHz. Attachment of a DNA molecule caused the frequency to decrease by 75 Hz. What was the mass of the DNA? (Express your answer in units of kg as a pure number in scientific notation (e.g. 5.0E-11)