Electron Microscopes

The smallest detail a microscope can show, its resolution, is limited by diffraction. Details much smaller than the wavelength of the waves used cannot be resolved, because the waves diffract around them and the images of neighbouring points blur together.Visible light has wavelengths of about 400 nm to 700 nm, so an optical microscope cannot resolve detail finer than roughly 200 nm. Individual atoms, about 10^-10 m across, are far too small to see.An electron microscope uses a beam of electrons instead of light. The electrons are accelerated through a large potential difference, often tens of kilovolts, so they have a large momentum and a de Broglie wavelength much shorter than that of light. This gives a far better resolution.Magnetic (or electric) fields act as lenses to focus the electron beam, since glass lenses cannot focus electrons. The instrument is evacuated so that the electrons are not scattered by air molecules.Worked exampleElectrons are accelerated from rest through 5.0 kV. Calculate their de Broglie wavelength.E_k = eV = 1.60 × 10^-19 × 5000 = 8.0 × 10^-16 Jp = √(2mE_k) = √(2 × 9.11 × 10^-31 × 8.0 × 10^-16) = 3.8 × 10^-23 kg m s^-1λ = h / p = 6.63 × 10^-34 ÷ 3.8 × 10^-23 = 1.7 × 10^-11 mThis is about 30 000 times shorter than the wavelength of green light (500 nm).Increasing the accelerating voltage increases the momentum of the electrons and shortens their wavelength, so even finer detail can be resolved.