To resolve an object in an electron microscope, the wavelength of the electrons must be close to the diameter of the object. what kinetic energy must the electrons have in order to resolve a protein molecule that is 8.80 nm in diameter? take the mass of an electron to be 9.11× 10–31 kg. you should first solve for the velocity of an electron that would have a de broglie wavength equal to the diameter of the protein. then calculate the energy of an electron with this velocity, using the equation for kinetic energy given in the hint below.

One kind of e-book display consists of millions of very small spheres that float in a thin fluid layer between two conducting transparent plates. each sphere is black on one side and white on the other, and possesses an electric dipole moment directed from the white side to the black. when an electric field is applied between the plates, the spheres rotate so that their dipole moment lines up with the field. depending on the fields direction, either the black or the white sides of th espheres can be made visible. the dipole moment of the spheres can be modeled as two opposite charges of magnitude 3.5 x 10^-15 c, separated by a distancce of 100 micrometers (um). what is the maximum possible torque on a sphere if the electric field between the transparent plates is 4.0 x 10^5 n/c