HOw does the quantum mechanical orbital differ from a bohr orvit for an electron in a hydrogen atom?

The quantum mechanical orbital and the Bohr orbit are two different models used to describe the behavior of electrons in a hydrogen atom.

The Bohr model, proposed by Niels Bohr in 1913, suggests that electrons are located in fixed circular orbits around the nucleus of an atom. Each orbit has a specific energy level, and electrons are only allowed to exist in these quantized orbits. The Bohr model successfully explained the spectral lines observed in hydrogen, but it had limitations. For example, it couldn't explain why electrons didn't radiate energy and spiral into the nucleus as classical physics predicted.

On the other hand, the concept of quantum mechanical orbitals considers the position and energy of an electron in a more probabilistic manner. According to quantum mechanics, electrons do not travel in neat, well-defined orbits. Instead, they are described by wave functions, which represent the probability distribution of finding an electron in a particular region around the nucleus.

Quantum mechanical orbitals are three-dimensional regions called probability clouds that indicate where an electron is likely to be found. These orbitals have various shapes, such as spheres, dumbbells, or more complex structures. Unlike the Bohr orbits, quantum mechanical orbitals do not have discrete energy levels. Instead, they have different energy states associated with them, forming an energy spectrum.

To calculate and understand quantum mechanical orbitals, physicists use mathematical equations called wave functions and employ techniques such as the Schrödinger equation to solve for these functions. Once the wave function is determined, the square of its absolute value gives the probability density of finding an electron in a particular location.

In summary, the main difference between the quantum mechanical orbital and the Bohr orbit is that the quantum mechanical orbital is a probabilistic description of where an electron is likely to be found, while the Bohr orbit proposed specific, fixed circular paths for electrons. The quantum mechanical orbital is derived from the principles of quantum mechanics and involves wave functions and probability distributions, while the Bohr orbit is based on classical physics and suggests well-defined paths for electrons.