Question

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 6.60 nm in diameter? Take the mass of an electron to be 9.11× 10−31 kg

Answer 1

diameter = 6.6 nm =6.6 x 10^-9 m = wavelength required

Momentum P = h / lamda                    ( by deborglie formula , where lamda is wavelength)

P = ( 6.625 x 10^-34 Js / 6.6x10^-9) = 1 x 10^-25 Jm-1s-1

now we have formula KE = P^2 / 2m      ( where KE is kinetic energy required, is mass of electron)

hence KE = ( 10^-25)^2 / ( 2 x 9.11 x 10^-31)

        = 5.53 x 10^-21 J