To resolve an object in an electron microscope, the wavelength of the electrons

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

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 2.30 nm in diameter? Take the mass of an electron to be 9.11x10 31 kg. Number

Explanation / Answer

we kow,

KE = (1/2)*m*v^2

KE = (m*v)^2/(2*m)

KE = p^2/(2*m)

==> p = sqrt(2*m*KE)

we know, wavelength of electron, lamda = h/p

diameter of molecule = h/sqrt(2*m*KE)

d = h/sqrt(2*m*KE)

d^2 = h^2/(2*m*KE)

==> KE = h^2/(2*m*d^2)

= (6.626*10^-34)^2/(2*9.11*10^-31*(2.3*10^-9)^2)

= 4.56*10^-20 J

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