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A light microscope cannot show details much smaller than the wavelength of light. Electrons, as de Broglie predicted, also behave as waves, with wavelengths thousands of times shorter. Ernst Ruska turned that into an instrument. This post covers his life, how a coil of wire focuses electrons, a worked example of the electron wavelength, and what a student can take from how he worked.
Who was Ernst Ruska?
His Nobel facts page gives his birth as 25 December 1906 in Heidelberg, and his death in West Berlin in May 1988. In his Nobel autobiography he describes studying electronics in Munich from 1925 and then in Berlin, where he worked on high-voltage and vacuum technology under Dr Max Knoll. He received half of the 1986 Nobel Prize in Physics "for his fundamental work in electron optics, and for the design of the first electron microscope". The other half went to Gerd Binnig and Heinrich Rohrer for the scanning tunnelling microscope.
How can a coil of wire act as a lens?
Ruska's first scientific work, in 1928 and 1929, tested Hans Busch's theory that the magnetic field of a current-carrying coil focuses electrons. He found that wrapping the coil in an iron casing shortened the focal length. That led to the pole-piece lens, which he says has been used in all magnetic high-resolution electron microscopes since.
The 1986 press release adds that with two coils in series he reached a magnification of fifteen times. Modest, but it was the first prototype. Knoll and Ruska described it in Das Elektronenmikroskop in 1932. In 1933 Ruska built an instrument that, in his words, "for the first time gave better definition than a light microscope".
How did it become a working tool?
Ruska saw that a university institute could not fund further development, so he moved to industry. With Bodo von Borries at Siemens he developed the first commercial electron microscopes, which reached the market in 1939. His brother Helmut, a doctor, led work on uses in medicine and biology. Ruska's later Siemens model, the Elmiskop 1 of 1954, was used in more than 1,200 institutions.
Why do electrons show finer detail than light?
The press release gives the resolution of a light microscope as about 4,000 Å (400 nm), set by the wavelength of light. An electron of momentum p has de Broglie wavelength λ = h/p, as in the NCERT chapter on dual nature. Faster electrons, shorter waves.
Worked example: electron wavelength from accelerating voltage
An electron accelerated from rest through V volts gains kinetic energy eV = p²/2m, so p = √(2meV) and λ = h/√(2meV).
At 100 V. 2meV = 2 × 9.11 × 10⁻³¹ × 1.602 × 10⁻¹⁹ × 100 = 2.92 × 10⁻⁴⁷. Square root: 5.40 × 10⁻²⁴ kg m/s. λ = 6.63 × 10⁻³⁴ / 5.40 × 10⁻²⁴ = 1.23 × 10⁻¹⁰ m = 0.123 nm.
Shortcut. Putting in the constants gives λ ≈ 1.227/√V nm, with V in volts.
At 10,000 V. √10,000 = 100, so λ ≈ 0.0123 nm.
Compare with light. Green light has λ = 550 nm. The ratio is 550 / 0.0123 ≈ 45,000.
A limit of the formula. At 100,000 V the same formula gives 0.00388 nm, but the electron is then fast enough for relativity to matter, and the correct value is about 0.0037 nm.
In practice the resolution is much coarser than the electron wavelength: the press release puts the practical limit at about 1 Å.
What mistakes do students make here?
Using kV directly. 10 kV is 10,000 V in the formula.
Using a photon formula. For electrons λ = h/p, not λ = hc/E.
Using the proton mass or forgetting the factor 2 in 2meV.
Confusing magnification with resolution. Magnifying a blurred image adds no detail.
De Broglie's relation is in Unit 17 of the JEE (Main) 2026 syllabus; check your year's syllabus. Practise with our de Broglie wavelength problems, and read how the idea began in our post on de Broglie's matter waves. If you want a check on each line of your working, the Fermi Problem Library has worked problems with a step-by-step solver that explains the reasoning rather than printing an answer.
What can a student take from how he worked?
Start small. A magnification of fifteen times was the first step to a new kind of instrument.
Test the theory you were taught. His first project checked Busch's lens theory and improved it.
Take your idea where it can grow. He moved to industry when a college lab could not build what was needed.
Work with people who will use your tool. His brother's medical work showed what the microscope could do.
Next step: work out the electron wavelength at 2,500 V and compare it with the size of an atom, about 0.1 nm.
