The Bohr model describes electrons moving in fixed orbits around the nucleus. This representation was crucial in advancing our understanding of atomic structure.

In the Bohr model, the nucleus, which is at the center of the atom, is made up of both protons and neutrons. Electrons orbit around this central core.

The Bohr model posits that electrons can only reside in specific orbits, corresponding to fixed energy levels. This concept of quantization was key to explaining atomic emission spectra.

Bohr developed his model based on studies of the hydrogen atom, which, with its single electron, provided a clear and simple system to analyze. This work laid the groundwork for modern atomic theory.

In the Bohr model, electrons transition between fixed energy levels by absorbing or emitting quantized packets of energy. This explains the discrete nature of the observed spectral lines.

The radius of an electron's orbit in the Bohr model is determined by its principal quantum number, which defines the energy level. This quantization establishes discrete distances from the nucleus where electrons can be found.

When an electron transitions to a higher orbit, it requires an input of energy to overcome the attractive force of the nucleus. This energy absorption is quantized, meaning only specific amounts of energy are allowed for the transition.

The energy levels of the hydrogen atom in the Bohr model are given by E = -13.6 eV divided by the square of the principal quantum number. This formula shows that energy becomes less negative as n increases, indicating higher energy levels.

When an electron drops from a higher energy level to a lower one, the atom emits energy in the form of a photon. The energy carried by the photon equals the difference between the two energy levels.

The Bohr model introduced the revolutionary concept that electron energy levels are quantized. This idea was crucial in the development of quantum mechanics and helped explain discrete atomic spectra.

The wavelength of the emitted light is directly related to the energy difference between the initial and final electron orbits. Larger energy differences produce photons with shorter wavelengths, resulting in the distinct spectral lines observed.

The Bohr model excelled in describing the hydrogen atom because it possesses only one electron. This simplicity avoids the complexities introduced by interactions among multiple electrons, such as electron-electron repulsions.

A larger principal quantum number signifies that an electron is in a higher energy state and farther from the nucleus, resulting in a larger orbit. This is a fundamental concept in the Bohr model, illustrating quantized energy levels.

The Bohr model successfully explains the emission spectrum of the hydrogen atom. When electrons transition between quantized energy levels, they emit photons at specific wavelengths, resulting in distinct spectral lines.

Only specific wavelengths are emitted because electrons are allowed to exist only in certain energy levels. When they transition between these levels, the energy difference corresponds to photons of defined wavelengths.

Calculating the energy values using the formula E = -13.6 eV/n² shows that the drop from n=4 to n=2 produces a larger energy difference compared to the drop from n=3 to n=2. Therefore, the n=4 to n=2 transition results in emission of a higher-energy photon.

The Bohr model introduced the concept of quantized angular momentum, which restricts electrons to certain stable orbits where they do not radiate energy continuously. This breakthrough helped resolve the classical physics dilemma regarding electron collapse into the nucleus.

In the Bohr model, as the principal quantum number increases, the energy levels become less negative, indicating higher energy states. Therefore, an electron in n=5 has a higher energy level than one in n=2.

For hydrogen-like atoms, the energy levels are proportional to the square of the nuclear charge, making them more negative with an increase in charge. This leads to larger energy gaps between the quantized levels.

In multi-electron atoms, the repulsion between electrons introduces additional forces that complicate the clear, quantized energy level structure seen in the hydrogen atom. This electron-electron interaction is the primary challenge in extending the Bohr model to more complex atoms.