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Every chemistry and physics student meets E = hf early, usually as a line to memorise. The man who wrote it down did not think, at first, that he had changed physics. Max Planck introduced energy quanta in 1900 as a mathematical step to make a formula work, and he spent years trying to explain them away. This post covers what he actually did, why he doubted it, and how to use his constant in a calculation.
What problem was Planck trying to solve?
When an object is heated it glows, and the spread of colours it gives off depends on its temperature, not on what it is made of. The Nobel Prize summary of Planck's work notes that calculating this spectrum with the physics of the day gave an impossible answer: the radiation at high frequencies came out infinite.
Planck's own route was different from the textbook story. In Physics World, the historian Helge Kragh explains that Planck cared most about the second law of thermodynamics and entropy, and wanted a rigorous derivation of the radiation law rather than just a formula that fitted. By 1899 he had a derivation of Wien's law. Then measurements in Berlin showed it failed at long wavelengths. In his Nobel lecture, Planck credits Heinrich Rubens and Ferdinand Kurlbaum, whose infrared measurements revealed the mismatch.
What did Planck present in October and December 1900?
On 19 October 1900, Kragh writes, Planck presented a new radiation law to the German Physical Society that matched the data, including in the infrared. He later called it, in his Nobel lecture, a "happily chosen interpolation formula", and he set out to find the physics behind it.
On 14 December 1900 he presented that derivation. To count the ways energy could be shared among his model oscillators, he divided the total energy into finite equal parts, each equal to a constant times the frequency. That constant is h. The full paper appeared in Annalen der Physik in 1901.
Did Planck believe energy really came in packets?
Not at first. Kragh quotes a 1931 letter in which Planck described the step as "a purely formal assumption". Planck published nothing on black-body radiation or quantum theory between 1901 and 1906, and only around 1908, influenced by Hendrik Lorentz, did he accept that the quantum was something classical physics could not explain.
Planck said much the same himself. In his Nobel lecture he described the quantum of action as something that "proved elusive and resistant to all efforts to fit it into the framework of classical theory." He then set out the choice plainly: either the quantum was a fiction, or it was real and physics had to change. His verdict: "Experiment has decided for the second alternative."
The people who made that decision possible were others. Planck's lecture names Einstein first, whose 1905 light-quantum idea explained the photoelectric effect, and Niels Bohr's 1913 atom. Planck received the 1918 Nobel Prize in Physics "in recognition of the services he rendered to the advancement of Physics by his discovery of energy quanta", presented a year later, in 1919.
Worked example: how much energy is in one quantum of light?
Planck's relation is E = hf. For light, f = c/λ, so E = hc/λ.
Take green light with λ = 500 nm.
Convert the wavelength: 500 nm = 500 × 10⁻⁹ m = 5.00 × 10⁻⁷ m.
Use h = 6.626 × 10⁻³⁴ J s and c = 3.00 × 10⁸ m/s.
E = (6.626 × 10⁻³⁴ × 3.00 × 10⁸) / (5.00 × 10⁻⁷) = 3.98 × 10⁻¹⁹ J.
In electron volts, divide by 1.602 × 10⁻¹⁹ J/eV: E ≈ 2.48 eV.
Planck's first value, given in his Nobel lecture, was 6.55 × 10⁻²⁷ erg s, which is 6.55 × 10⁻³⁴ J s. Today's value, fixed exactly by NIST and the SI, is 6.62607015 × 10⁻³⁴ J s. His 1900 estimate was about 1% low.
Common mistakes to avoid:
Forgetting the nm conversion. Using 500 instead of 5.00 × 10⁻⁷ gives an answer off by a factor of a billion.
Mixing J and eV. Many options in exams are in eV. Convert at the end, not halfway.
Using f and λ interchangeably. Energy rises with frequency and falls with wavelength.
Planck's quantum theory, the photoelectric effect and atomic spectra all sit together in NCERT Class 11 Chemistry, Unit 2, and the JEE (Main) 2026 syllabus lists the photoelectric effect and dual nature of radiation in physics. Check the current year's syllabus for your exam. When you are ready for exam-style questions, our guide to photoelectric effect problems uses this same E = hf step.
What can a student take from Planck's way of working?
Three habits stand out.
He took a mismatch with data seriously. His 1899 derivation was elegant, and he dropped it when the infrared data disagreed.
He separated "it fits" from "I understand why". He had a working formula in October and was still unsatisfied. That is the difference between matching an answer key and knowing the physics.
He let evidence settle his doubts. He did not want the quantum to be real, and he accepted it when the experiments of others left no other choice.
If black-body curves are hard to picture from a textbook graph, the Fermi Simulation Lab has interactive simulations for ideas that are easier to see than read. For the theory itself, read our post on Einstein's 1905 papers, where the quantum became physical.
Try it now: calculate the energy of a 400 nm violet photon and a 700 nm red photon in eV, and check that violet comes out higher.
