1. Blackbody Radiation:
* Problem: Classical physics predicted that a blackbody (a perfect absorber and emitter of radiation) should radiate energy at all frequencies, leading to the "ultraviolet catastrophe" where infinite energy would be emitted.
* Solution: Quantum mechanics provided a solution by quantizing energy, meaning that energy could only exist in discrete packets. This explained the observed distribution of blackbody radiation.
2. Photoelectric Effect:
* Problem: Classical physics predicted that increasing the intensity of light should increase the energy of emitted electrons. However, experiments showed that only the frequency of light affected the electron's energy.
* Solution: Einstein explained this using the concept of photons, packets of light energy, which demonstrated the particle nature of light.
3. Atomic Spectra:
* Problem: Classical physics failed to explain the discrete spectral lines emitted by atoms when excited. It predicted a continuous spectrum.
* Solution: The Bohr model of the atom explained these spectral lines by quantizing the energy levels of electrons orbiting the nucleus. Quantum mechanics later provided a more sophisticated description of atomic structure.
4. Specific Heat of Solids:
* Problem: Classical physics predicted that the specific heat of solids should be constant at all temperatures, but experiments showed it decreased at low temperatures.
* Solution: Quantum mechanics explained this by considering the quantization of vibrational energy in solids.
5. Wave-Particle Duality:
* Problem: Classical physics viewed light as a wave and matter as particles. Experiments, like the double-slit experiment, showed that both light and matter can exhibit wave-like and particle-like behavior.
* Solution: Quantum mechanics reconciled these seemingly contradictory behaviors by describing both light and matter as having both wave-like and particle-like properties.
6. Relativity:
* Problem: Classical mechanics assumed that time and space are absolute. Special relativity, developed by Einstein, showed that time and space are relative and depend on the observer's frame of reference. General relativity extended this to include gravity, describing it as a curvature of spacetime.
* Solution: Relativity is not strictly a failure of classical mechanics, but rather an expansion of it. It is essential for understanding the behavior of objects moving at very high speeds or in strong gravitational fields.
In summary: While classical mechanics is a powerful tool for describing the motion of objects in everyday life, it breaks down at the microscopic level and at very high speeds. Quantum mechanics and relativity provide a more complete description of physical phenomena at these scales.
