## Electron microscope

### Task number: 4377

Electron microscope can distinguish objects of scales around ten times bigger than the wavelength of used electrons. One microscope uses electrons accelerated to 10 keV. What is the smallest structure the microscope can distinguish?

#### Hint

How are the energy of a particle and the wavelength of the corresponding de Broglie wave related?

#### Solution

The relation between the kinetic energy of the particle

\[\lambda=\frac{h}{\sqrt{2mE}}\,,\]*E*and wavelength*λ*corresponding to de Broglie wave is given by formulawhere

*m*is the mass of the particle and*h*is the Planck’s constant.We use the mass of an electron

\[\lambda=\frac{6.626\,\cdot\,10^{-34}}{\sqrt{2\,\cdot\,9.11\,\cdot\,10^{-31}\,\cdot\,1.602\,\cdot\,10^{-15}}}\ \mbox{m}\,=\frac{6.626}{\sqrt{2\,\cdot\,9.11\,\cdot\,1.602}}\ 10^{-11}\ \mbox{m}\,\dot{=}\,1.2\,\cdot\,10^{-11}\ \mbox{m}\,\dot{=}\, 0.01\ \mbox{nm}\,.\]*m*= 9.11·10^{−31}kg. We obtainTherefore the resolution power of the microscope is at least approximately tenths of a nanometer which are the units called ångström.

#### Answer

The resolution power of the electron microscope is approximately 10^{−10}m.#### Refrence

Play with the application available at http://learn.genetics.utah.edu/.../cells/scale/ and think about what is possible to observe with this type of microscope.