Numerous places:
1) photo-electric effect.
2) black-body radiation spectrum.
3) spectrum of hydrogen emissions.
4) interference patterns of electrons through a slit.
5) compton scattering.
All of the above can be easily explained by the existence of 'quanta,' but are impossible to explain through purely classical means.
Classical mechanics fails to accurately describe the behavior of particles at the quantum level, unlike Schrödinger's equation which can predict the behavior of particles based on their wave functions. Classical mechanics does not account for wave-particle duality, uncertainty principle, and quantum superposition which are crucial in understanding quantum systems. Schrödinger's equation provides a more comprehensive and accurate description of particle behavior at the atomic and subatomic levels.
Classical mechanics assumes that light energy is a self-propagating, harmonic wave of electro-magnetic fields. It assumes that there is no limit to how small the energy in a light beam can be. QM, on the other hand, assumes there is a limit to how small the energy within a "chunk" of light can be, and that size is given by the frequency of the light times Planck's Constant. With this assumption, the formula for frequency shift of scattered photons as a function of angle can be easily explained. Using only classical mechanics, deriving the formula is impossible.
Unlike other physical theories, quantum mechanics was the invention of not only one or two scientists. Planck, Einstein, Bohr, Heisenberg, Born, Jordan, Pauli, Fermi, Schrodinger, Dirac, de Broglie, Bose are the scientists that made notable contributions to the invention of quantum theory. The axioms of quantum mechanics provide a consistent framework in which it is once again possible to predict the results of experiment, at least statistically.Its fundamental features are that a property does not exist unless it is measured, and that indeterminacy is a fundamental property of the universe. The main merit of QM is that its predictions -- such as that for the two slit experiment -- perfectly match the results, while classical mechanics fails to do so. For a scientist, nothing else much matters.
The Bohr model is inaccurate because it is based on classical mechanics, which does not fully explain the behavior of electrons in atoms. It also fails to account for electron-electron interactions and the wave-like nature of particles. Quantum mechanics provides a more accurate description of the behavior of electrons in atoms.
One problem is that the classical model of the atom fails to explain the stability of the electron orbits around the nucleus, as predicted by classical electromagnetism. Another problem is that it does not account for the wave-particle duality of electrons and other subatomic particles, which is described by quantum mechanics.
Classical physics fails to accurately describe phenomena at the quantum scale, like particles behaving as waves and existing in superpositions. Quantum mechanics, with principles like wave-particle duality and quantization of energy levels, provides a more comprehensive framework to explain such phenomena. Thus, the transition from classical to quantum physics occurs due to the limitations of classical physics in describing the behavior of particles at the quantum level.
Classical mechanics fails to accurately describe phenomena on very small scales, such as those in the quantum realm. Additionally, classical mechanics cannot explain certain phenomena related to high speeds or strong gravitational forces, leading to the development of theories like general relativity. Overall, classical mechanics is limited in its ability to describe the full range of physical phenomena observed in the universe.
Classical mechanics fails to accurately describe the behavior of particles at the quantum level, unlike Schrödinger's equation which can predict the behavior of particles based on their wave functions. Classical mechanics does not account for wave-particle duality, uncertainty principle, and quantum superposition which are crucial in understanding quantum systems. Schrödinger's equation provides a more comprehensive and accurate description of particle behavior at the atomic and subatomic levels.
Classical mechanics assumes that light energy is a self-propagating, harmonic wave of electro-magnetic fields. It assumes that there is no limit to how small the energy in a light beam can be. QM, on the other hand, assumes there is a limit to how small the energy within a "chunk" of light can be, and that size is given by the frequency of the light times Planck's Constant. With this assumption, the formula for frequency shift of scattered photons as a function of angle can be easily explained. Using only classical mechanics, deriving the formula is impossible.
Unlike other physical theories, quantum mechanics was the invention of not only one or two scientists. Planck, Einstein, Bohr, Heisenberg, Born, Jordan, Pauli, Fermi, Schrodinger, Dirac, de Broglie, Bose are the scientists that made notable contributions to the invention of quantum theory. The axioms of quantum mechanics provide a consistent framework in which it is once again possible to predict the results of experiment, at least statistically.Its fundamental features are that a property does not exist unless it is measured, and that indeterminacy is a fundamental property of the universe. The main merit of QM is that its predictions -- such as that for the two slit experiment -- perfectly match the results, while classical mechanics fails to do so. For a scientist, nothing else much matters.
Classical physics fails to explain the photoelectric effect because it is based on the wave theory of light, which predicts that the energy of a wave is proportional to its intensity. However, the photoelectric effect shows that the energy of ejected electrons is dependent on the frequency of light, not its intensity, as predicted by quantum theory.
i think quantum effects is temperature dependent, the question will be at which temperature do we expect quantum effects to become important. The classical theory fails at a certain temperature then quantum theorie should be used. Classical statistical mechanics tells us that the distance between particles in a gas under standard-conditions is of the order of 10∙10-9 m=10nm. In order to observe quantum mechanical effects in such a gas we have to reduce the temperature drastically. Zero K is the lowest possible temperature, since it corresponds to particle velocity of zero...
Classical physics relies on deterministic laws, continuous quantities, and a distinct separation between particles and waves. However, it fails to explain certain phenomena, such as the behavior of subatomic particles in quantum mechanics. Deviation from classical physics becomes evident in experiments like the double-slit experiment, where particles exhibit wave-like behavior, challenging the classical notion of determinism and separate particle-wave duality. This deviation led to the development of quantum mechanics to describe the behavior of particles at the microscopic level.
The Bohr model is inaccurate because it is based on classical mechanics, which does not fully explain the behavior of electrons in atoms. It also fails to account for electron-electron interactions and the wave-like nature of particles. Quantum mechanics provides a more accurate description of the behavior of electrons in atoms.
Only that it doesn't manage to explain as much as modern physics (quantum physics, and the Theory of Relativity). Please note that for many practical purposes, classical physics is entirely adequate. For example, when the speeds involved are much lower than the speed of light, you can simply add velocities, rather than use the more complicated Lorentz transformations.
One problem is that the classical model of the atom fails to explain the stability of the electron orbits around the nucleus, as predicted by classical electromagnetism. Another problem is that it does not account for the wave-particle duality of electrons and other subatomic particles, which is described by quantum mechanics.
The classical free electorn theory is not able to explain conductivity for semiconducter and insulators