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I was reading about blackbody radiation and came across the following quote.

Planck did not believe in atoms, nor did he think the second law of thermodynamics should be statistical because probability does not provide an absolute answer, and Boltzmann’s entropy law rested on the hypothesis of atoms and was statistical. But Planck was unable to find a way to reconcile his Blackbody equation with continuous laws such as Maxwell’s wave equations. So in what Planck called “an act of desperation,” he turned to Boltzmann’s atomic law of entropy as it was the only one that made his equation work. Therefore, he used Boltzmann’s constant k and his new constant h to explain the Blackbody radiation law which became widely known through his published paper.

Source: https://en.wikipedia.org/wiki/Planck%27s_law#History

In atomic physics, the Bohr model or Rutherford–Bohr model, presented by Niels Bohr and Ernest Rutherford in 1913, is a system consisting of a small, dense nucleus surrounded by orbiting electrons—similar to the structure of the Solar System, but with attraction provided by electrostatic forces in place of gravity. It came after the solar system Joseph Larmor model (1897), the cubical model (1902), the Hantaro Nagaoka Saturnian model (1904), the plum pudding model (1904), the quantum Arthur Haas model (1910), the Rutherford model (1911), and the nuclear quantum John William Nicholson model (1912). The improvement over the 1911 Rutherford model mainly concerned the new quantum physical interpretation introduced by Haas and Nicholson, but forsaking any attempt to align with classical physics radiation.

The model's key success lay in explaining the Rydberg formula for the spectral emission lines of atomic hydrogen. While the Rydberg formula had been known experimentally, it did not gain a theoretical underpinning until the Bohr model was introduced. Not only did the Bohr model explain the reasons for the structure of the Rydberg formula, it also provided a justification for the fundamental physical constants that make up the formula's empirical results.

Source: https://en.wikipedia.org/wiki/Bohr_model

Question

It seems like most scientists of 19th century did not believe in atoms and possibly the belief in atoms started gaining traction around 1900.

How did they explain the radiation resulting from the materials during that era when the belief in atoms was not widespread? For example, when an object is heated why it starts emitting radiation at different wavelengths.

I'm asking this question because I think this 'misunderstanding' of pre-atomic era was at the core of ultraviolet catastrophe. The electrons emitting quanta of radiation when jumping from one orbital to another was an outcome of 1913 Bohr model atomic model.

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    $\begingroup$ ‘Atoms’ were well known from chemistry. Their nuclear structure was not known until Rutherford, Geiger, and Marsden in 1911. Lack of belief in atoms was not an issue. $\endgroup$
    – Jon Custer
    Jun 30, 2022 at 15:43
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    $\begingroup$ Thank you. The first quote mentions that Planck did not believe in atoms. I've read in the past that there were many 19th century scientists who did not believe in atoms but I only included the mention of Planck to make the point. $\endgroup$
    – PG1995
    Jun 30, 2022 at 23:43
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    $\begingroup$ Larmor formula was known from before Planck. Electromagnetic theory predicts that any changing electrical current produces an electromagnetic wave and it was well known that all matter was composed of positively and negatively charged fluids that could produce the currents. I would look at Boltzmann's papers for a clue, he derived Stefan-Boltzmann law using classical arguments (although he probably believed in atoms). $\endgroup$
    – Mauricio
    Jul 1, 2022 at 14:51
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    $\begingroup$ Thank you! But Larmor formula only came out around 1897 which showed that an accelerating charge radiated energy. But the scientists were doing work on blackbody related problems long before 1897 therefore they must have had some other explanation to explain for the radiation. $\endgroup$
    – PG1995
    Jul 1, 2022 at 21:50
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    $\begingroup$ Many scientists, including most chemists, did believe in atoms since the early 19th century, but there was also strong resistance among physicists (Mach et al.). The favored approach was to use general thermodynamic considerations, later also statistical mechanics, without specific material hypotheses you have in mind as explanations. That is what researchers of radiation did, from Kirchhoff to Planck and Jeans. The "ultraviolet catastrophe" is a historical fiction invented later, see How did Planck derive the black body radiation formula?. $\endgroup$
    – Conifold
    Jul 3, 2022 at 9:06

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