The Bohr Model and the Quantum Mechanical Model are two different ways to understand how electrons behave in atoms. Here are their main differences:

1. Electron Paths:

   • Bohr Model: In this model, electrons move in fixed paths called orbits around the center of the atom, which is called the nucleus. The energy levels of these orbits are specific values. They can be calculated using the formula $E_n = -\frac{13.6 \text{ eV}}{n^2}$, where $n$ is a number that represents the level of the orbit.

   • Quantum Mechanical Model: This model says that electrons are not in fixed paths. Instead, they are found in areas called orbitals. These orbitals are based on probabilities and are explained by something called wavefunctions.

2. Energy Levels:

   • Bohr Model: This model mainly works for hydrogen and shows energy levels that are separate and distinct from one another.

   • Quantum Mechanical Model: This model applies to all types of elements and describes energy levels using several numbers called quantum numbers. These include the principal quantum number ($n$), azimuthal quantum number ($l$), and magnetic quantum number ($m_l$).

3. Mathematics:

   • Bohr Model: This model uses basic math and ideas from classical physics to explain how electrons work.

   • Quantum Mechanical Model: This model uses more complicated math, including something called Schrödinger's equation, to explain how electrons behave.

In summary, the Quantum Mechanical Model gives a better and more accurate picture of what atoms look like and how electrons behave than the Bohr Model does.