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 .

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

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

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