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 2.40 nm in diameter?

Question

Take the mass of an electron to be #9.11x 10^-31# kg.

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Answer 1 · 2017-05-05T13:01:49

#sf(4.18xx10^(-20)color(white)(x)J)#

I will set the wavelength of the electron to be equal to the diameter of the protein molecule:

#sf(lambda=2.4xx10^(-9)color(white)(x)m)#

The de Broglie expression gives us:

#sf(lambda=h/(mv))#

#:.##sf(v=h/(mlambda))#

#sf(v=(6.63xx10^(-34))/(9.11xx10^(-31)xx2.4xx10^(-9))color(white)(x)"m/s")#

#sf(v=3.03xx10^(5)color(white)(x)"m/s")#

Kinetic energy #sf(=1/2mv^2)#

#:.##sf(KE=1/2xx9.11xx10^(-31)xx(3.03xx10^5)^2color(white)(x)J)#

#sf(KE=4.18xx10^(-20)color(white)(x)J)#