explain how the path of an electron differs in Bohr's model and in the modern model of the atom

In the modern model (quantum mechanics), the electron does not follow a path. It exists within a "probability cloud", the shape of which depends upon the energy and angular momentumn of the electron. It is impossible to tell where it is at a particular time.

In Bohr's model of the atom, electrons are assumed to travel in fixed circular orbits around the nucleus, much like planets orbiting the sun. These orbits are quantized, meaning that electrons can only occupy certain allowed energy levels or shells. When an electron absorbs or emits energy, it jumps between these energy levels.

On the other hand, in the modern model of the atom, known as the quantum mechanical model, electron paths are not described by fixed orbits or precise trajectories. Instead, electrons are treated as waves that exist in regions of probability called electron orbitals. These orbitals are three-dimensional regions around the nucleus where electrons are likely to be found.

The behavior of electrons in the modern model is mathematically described by wave functions, which give the probability distribution of finding an electron at a particular location. The shape and size of the electron orbitals depend on the energy and quantum numbers associated with each electron.

To determine the exact path or location of an electron in the modern model, one needs to solve the Schrödinger equation, which is a complex mathematical equation that describes the behavior of quantum systems. This equation takes into account various factors, such as the electron's energy, the properties of the atom, and the interactions among electrons.

In summary, Bohr's model assumes fixed circular orbits for electrons, while the modern model describes electrons as probability waves in electron orbitals. The modern model provides a more accurate and comprehensive understanding of the behavior of electrons in atoms, and it relies on solving the Schrödinger equation to determine their probable locations.