91Ó°ÊÓ

In Bohr's model of the atom, electrons move around the nucleus in specific, predefined paths called quantized orbits. These orbits exist at certain fixed distances from the nucleus and correspond to specific energy levels.
Unlike the concept of electrons moving randomly, Bohr's model suggests that electrons stay in stable orbits without radiating energy.

Think of these orbits as the rungs of a ladder. Just like you can't stand between the rungs of a ladder, an electron cannot exist between these quantized orbits. They are either in one orbit or another, and these transitions between orbits are what leads us to our next concept.

Bohr also introduced the idea that the angular momentum of an electron in these quantized orbits is itself quantized. Angular momentum is like the amount of ‘twist’ an electron has as it orbits the nucleus.

This means that the angular momentum isn't just any value but takes on specific, discrete values. To be exact, the angular momentum of an electron in an orbit is given by the formula: \[L = n \frac{h}{2\text{Ï€}} \] where \( n \) is an integer (1, 2, 3, ...), \( h \) is Planck's constant.

So, if an electron is in the first orbit, its angular momentum is \(\frac{h}{2\text{π}}\) . If it’s in the second orbit, it’s \(2\frac{h}{2\text{π}}\) , and so on. This quantization restricts electrons to specific orbits, maintaining the stability of the atom.

A significant part of Bohr's model is the explanation of how atoms emit or absorb light. When an electron jumps from one quantized orbit to another, it either emits or absorbs energy in the form of a photon.

The energy of this photon corresponds to the difference between the energy levels of the two orbits. The relation is given by: \[ E_{\text{photon}} = E_{\text{higher\text{ }orbit}} - E_{\text{lower\text{ }orbit}} \] which matches the energy needed for the transition.

For example, if an electron absorbs a photon, it gains enough energy to jump to a higher orbit. Conversely, if it emits a photon, it loses energy and falls to a lower orbit.

This process explains phenomena such as line spectra in atomic emission and absorption spectroscopy, where only specific wavelengths of light are emitted or absorbed by elements.