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Nuclear fission sits in every Class 12 physics syllabus, usually as an equation and an energy figure of about 200 MeV. That figure has a history. It was first worked out by two physicists in exile, using a model of the nucleus as a drop of liquid. This post covers who Lise Meitner was, how she and Otto Frisch explained fission, how to calculate the energy from a mass defect yourself and why she did not share the Nobel Prize.
Who was Lise Meitner?
The Atomic Heritage Foundation's profile gives her dates as 1878 to 1968. She was Austrian, and in 1906 she became the second woman to receive a doctorate from the University of Vienna. She moved to Berlin, attended Max Planck's lectures, became his assistant and began a long collaboration with the chemist Otto Hahn. In 1913 she took a permanent position at the Kaiser Wilhelm Institute.
Her Austrian citizenship let her stay in Germany after 1933 longer than many colleagues. In 1938 she was taken secretly across the Dutch border, leaving her possessions behind, and went on to Stockholm.
What did Hahn and Strassmann find?
Hahn and Fritz Strassmann kept working in Berlin, bombarding uranium with neutrons. In January 1939 they published a paper in Die Naturwissenschaften on the alkaline earth metals formed in these experiments. As Meitner and Frisch summarised it, Hahn and Strassmann "were forced to conclude that isotopes of barium (Z = 56) are formed" from uranium (Z = 92). That was hard to understand, because nuclei were only known to emit particles with one or two charges.
How did Meitner and Frisch explain fission?
Meitner discussed the result with her nephew Otto Frisch, also a physicist. Their letter, Disintegration of Uranium by Neutrons: a New Type of Nuclear Reaction, appeared in Nature on 11 February 1939.
They treated the heavy nucleus like a liquid drop, whose surface tension is weakened by its electric charge. So the uranium nucleus "has only small stability of form, and may, after neutron capture, divide itself into two nuclei of roughly equal size". The two pieces would push each other apart electrically. In their words, "These two nuclei will repel each other and should gain a total kinetic energy of c. 200 Mev., as calculated from nuclear radius and charge." They added that this energy should be available from the difference in packing fraction, closely related to what you now call binding energy per nucleon, between uranium and elements in the middle of the periodic table. They named the process fission.
Worked example: energy from the mass defect
Take one common fission: ²³⁵U + n → ¹⁴¹Ba + ⁹²Kr + 3n. Use atomic masses from the NIST isotope tables:
²³⁵U: 235.043930 u
¹⁴¹Ba: 140.914403 u
⁹²Kr: 91.926173 u
neutron: 1.008665 u
Mass before: 235.043930 + 1.008665 = 236.052595 u.
Mass after: 140.914403 + 91.926173 + 3 × 1.008665 = 235.866571 u.
Mass defect: 236.052595 − 235.866571 = 0.186024 u.
Energy: 0.186024 × 931.5 MeV/u ≈ 173 MeV.
That is the same size as Meitner and Frisch's estimate. The exact figure depends on which pair of fragments forms, and the fragments release more energy later as they decay.
Common mistakes to avoid:
Forgetting the incoming neutron on the left side, or miscounting neutrons on the right. Check that mass numbers balance: 235 + 1 = 141 + 92 + 3.
Worrying about electrons. Atomic masses include electrons, but 92 = 56 + 36, so they cancel.
Rounding masses too early. The defect is less than 0.1% of the total mass. Round to two decimal places and the answer is badly wrong.
For the next step, from one fission to many, read our post on the first nuclear chain reaction. If binding energy per nucleon is the shaky part, the Fermi Concept Library covers every concept in physics with its own lesson, so you can revise that one idea before trying more problems.
Why did Meitner not share the Nobel Prize?
The 1944 Nobel Prize in Chemistry went to Hahn alone, "for his discovery of the fission of heavy nuclei". The Nobel Prize nomination archive lists Meitner as a nominee in 49 nominations across physics and chemistry, from nominators including Max Planck, Niels Bohr and the Indian chemist Nil Dhar. She never received the prize.
Other honours came. Element 109 is named meitnerium, as the Royal Society of Chemistry notes. Frisch wrote her epitaph: "Lise Meitner: a physicist who never lost her humanity."
What can a student learn from how Meitner worked?
Ask what a result means physically. Hahn had the chemistry. Meitner asked what the nucleus must be doing for the chemistry to be true.
Use a simple model first. A liquid drop is not a perfect picture of a nucleus, but it was good enough to give the right energy.
Check one estimate with another. Repulsion and mass difference gave the same answer.
Practice this week: repeat the mass-defect calculation for ²³⁵U + n → ¹⁴⁰Xe + ⁹⁴Sr + 2n using NIST masses, and compare your answer with 173 MeV.
