$1.$ Calculate the interaction energy per unit area between two silicon surfaces $($A $=2010-20$ J$)$ at a separation D $=0\mathrm{.}5$ nm in air. Use this result to estimate the force between a silicon AFM tip with the surface of a silicon wafer, below $($scale bar $=5$ nm$).$ What are the assumption you make for this calculation?

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$2.$ A sphere composed of polyvinylchloride $($PVC$,$ A $=7\mathrm{.}510-20$ J$,$ $=1300$ kg m$-3,$ rVDW ~$0\mathrm{.}17$ nm$)$ is adhered to the underside of a smooth sheet of the same material against the force of gravity. The largest radius, R$,$ of sphere that will remain adhered to the surface against the force of gravity is $1\mathrm{.}5$ mm$.$ On which planet are we most likely to be: Earth, Mercury $($the smallest of the planets$),$ or Jupiter $($the largest of the planets$)?$

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