(Solved): Determine the mass of the DNA molecule in Dalton. In recent years it has become possible to "weigh" ...

In recent years it has become possible to "weigh" individual DNA molecules by measuring the influence of their mass on a nanoscale cantilever (oscillator), as shown in the figur below. The figure shows a thin rectangular cantilever etched out of silicon. The cantilever has a mass $M$, where $M=3.7\times 10^{?16}\mathrm{kg}$. If pulled and released, the end of the cantilever vibrates, moving up and down like a diving board after a jump. When bathed with DNA molecules that bind to the cantilever's surface, the addition of the DNA mass causes a small but measurable change in its oscillation frequency. For an experiment, the nano-cantilever was initialis vibrating at exactly $12\mathrm{MHz}$. After attachment of a DNA molecule, its frequency of oscillation decreased by $50\mathrm{Hz}$. Determine the mass of the DNA molecule in Daltons? For example, $1\mathrm{kg}=6.022\times 10^{26}$ Daltons. Hint The nano-cantilever can be modeled as block of mass $m_c$ oscillatirg on a spring with constant $k$, where $m_c=1/3\mathrm{M}$. The spring constant $k$ does not change when mass is added to the spring So the value of the spring constant is the some before and after DNA is odded. In other words, calculate $k$ of the nano-cantilever sytern before the moss of the DNA was added to it.