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 2.70 nm in diameter? Take the mass of an
electron to be 9.11x10^{-31}kg.

Answer #1

Given : wavelength (?) = 2.70 nm (Convert to m )

Mass of electron = 9.11x10^{-31}kg.

We use deBroglie equation to find out momentum.

. ? = h/ P ? is wavelength in m , h = Planks constant = 6.626 E-34 J s

Lets convert ? to m

?(in m) = 2.70 nm * 10^{-9} m / 1
nm
( 1m = 10^9 nm )

? = 2.70 E-9 m

Lets find momentum (P)

P= h/ ?

= 6.626 E-34 Js / 2.70 E-9 m

= 2.45E-25 kg
m/s ( 1J= kg
m^{2} s^{-2} )

Now we know

KE=

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