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, E k, must the electrons have in order to resolve a protein molecule that is 2.70 nm in diameter? Take the mass of an electron to be 9.11 * 10 - 31 kg.

3.32 * 10^-20 J

Explanation:

Let the wavelength of the electron be equal to the diameter if the protein molecule.

λ = 2.7 * 10 ^ - 9 m

using De Broglie's equation

λ = h / mv

Where

λ = wavelength

h = Planck's constant

m = mass of the particle

v = velocity of movement of the particle

Then ...

v = h / mλ

v = (6.63 * 10^-34) / [ (9.11 * 10^-31) * (2.7 * 10^-9) ]

v = 2.70 * 10^5 m/s

KE = Kinetic Energy

KE = 1/2mv²

KE = 1/2 (9.11 * 10^-31) * (2.7 * 10^5) ²

KE = 3.32 * 10^-20 J

KE = 3.308*10^-20J

Explanation:

Let the wavelength of the electron equal the diametre of the protein molecule

Wavelength = 2.70 nm = 2.70 * 10^-7m

The de Brogule expression gives ud:

Wavelength = h / mv

V = h/m * wavelength

Where h is plank's constant

V = (6.63*10^-11) / (9.11*10^-31) (2.70*10^-9)

V = (6.63*10^-34) / (2.4587*10^-30)

V = 2.695*10^5m/s

KE = 1/2mv^2

KE = 1/2 (9.11*10^-31) (2.695 * 10^5) ^2

KE = 1/2 * (9.11*10^-31) (7.26*10^10)

KE = 3.308*10^-20J