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 5.80 nm in diameter? Take the mass of an electron to be 9.11× 10–31 kg.

Answer 1

According to de Broglie wave length, = h/mv
Where

h = plank's constant = 6.625x 10^-34 Js

= wave length = diameter of object = 5.80 nm = 5.80x10^-9 m

m = mass of object(electron) = 9.11× 10^–31 kg

v = velocity of object = ?

Plug the values we get

v = h / m

= (6.625x 10^-34 Js) / (9.11× 10^–31 x 5.80x10^-9 m )

= 125.4x10³ m/s

Kinetic energy , KE = (1/2) mv²

                             = (1/2)x 9.11× 10^–31 kgx(125.4x10³ m/s)²

                            = 7.16x10^-21 J