Question A: A sphere of silicon (density = 2330 kg/m3) is in close proximity to a...

Transcribed Image Text:

Question A: A sphere of silicon (density = 2330 kg/m3) is in close proximity to a solid. There is a van der Waals attraction between the solid and sphere, with an energy given by E(x): = HR 6x Taking the derivative yields the van der Waals force between the sphere and the solid. F(x) = HR 6x2 How big (what radius R ?) can the silicon sphere be so that the force of attraction balances the downward force of gravity on the sphere, when they are separated by a. x 1 nm, and b. x = 10 nm. H is the HAMAKER constant = 10-19 Joules. solid 2R Gravity, g = 9.8 m/s silicon sphere x Question A: A sphere of silicon (density = 2330 kg/m3) is in close proximity to a solid. There is a van der Waals attraction between the solid and sphere, with an energy given by E(x): = HR 6x Taking the derivative yields the van der Waals force between the sphere and the solid. F(x) = HR 6x2 How big (what radius R ?) can the silicon sphere be so that the force of attraction balances the downward force of gravity on the sphere, when they are separated by a. x 1 nm, and b. x = 10 nm. H is the HAMAKER constant = 10-19 Joules. solid 2R Gravity, g = 9.8 m/s silicon sphere x