Quantum theory provides an explanation for the line spectra of atoms through the understanding of energy quantization and the behavior of electrons within atoms. The line spectra, also known as atomic spectra or emission spectra, are the distinct and discrete wavelengths of light emitted or absorbed by atoms.
According to quantum theory, electrons in atoms occupy specific energy levels or orbitals. These energy levels are quantized, meaning they can only have certain discrete values. When an electron transitions from one energy level to another, it either emits or absorbs energy in the form of photons (light quanta). The energy of each emitted or absorbed photon corresponds to the energy difference between the initial and final energy levels.
The specific wavelengths of light emitted or absorbed by atoms in their line spectra can be explained by the quantization of energy levels. Each transition between energy levels corresponds to a specific change in energy, and this change determines the wavelength of light associated with the transition.
The energy levels of electrons in atoms are determined by the atomic nucleus and the electron's interaction with it. The Schrödinger equation, a fundamental equation in quantum mechanics, is used to solve for the allowed energy levels and wavefunctions (describing the probability distribution of finding an electron) of the electrons in an atom.
The line spectra observed for different elements and atoms arise from the unique arrangement of energy levels and the corresponding transitions that are allowed. Each element has a distinct set of energy levels, resulting in a unique pattern of emission or absorption lines in its spectrum. These lines correspond to specific transitions between the energy levels of the atom.
The line spectra observed experimentally can be accurately predicted and explained by quantum theory, providing a quantitative understanding of the wavelengths and intensities of the spectral lines. The Bohr model, for example, was an early application of quantum theory that successfully explained the line spectra of hydrogen atoms.
In summary, quantum theory explains the line spectra of atoms by considering the quantization of energy levels for electrons in atoms. The specific wavelengths observed in the line spectra result from the discrete energy transitions between these levels, which can be calculated using quantum mechanics.