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, E k , must the electrons have in order to resolve a protein molecule that is 7.40 nm in diameter? Take the mass of an electron to be 9.11 × 10 − 31 kg .

Answer 1

The kinetic energy must the electrons have in order to resolve a protein molecule is E = 4.36 ×
`10^(-21)` J

Step-by-step explanation:

Given data

`\lambda = 7.4` ×
`10^(-9)` m

Mass of electron = 9.1 ×
`10^(-31)` kg

From de-broglie theory

`\lambda = (h)/(mv)`

`v = (h)/(m \lambda)`

Put all the values in above formula we get

`v = (6.62 (10^(-34) ))/((7.4)(10^(-9) )(9.1)(10^(-31) ))`

v = 0.98 ×
`10^(5) (m)/(s)`

Kinetic energy is given by

`E = (1)/(2) m v^(2)`

`E = (1)/(2) (9.1)0.98^(2)` ×
`10^(-21)` J

E = 4.36 ×
`10^(-21)` J

Therefore the kinetic energy must the electrons have in order to resolve a protein molecule is E = 4.36 ×
`10^(-21)` J