Final answer:
The Bohr model and the quantum mechanical model of the hydrogen atom both describe the distribution of electrons but differ in their mathematical rigor and consideration of quantum principles.
Step-by-step explanation:
The Bohr model and the quantum mechanical model of the hydrogen atom are similar in that they both describe the distribution of electrons around the nucleus and incorporate the concept of discrete energy levels. However, they differ in terms of their mathematical rigor and their consideration of quantum principles.
The Bohr model, proposed by Niels Bohr, describes electrons as particles with definite orbits, with quantized energies and angular momentum. It assumes that the electrons move in circular orbits around the nucleus and do not emit or absorb electromagnetic radiation while in those orbits. The Bohr model gives a good explanation for the observed spectral lines of hydrogen.
In contrast, the quantum mechanical model, based on the wave-particle duality of electrons, incorporates probability distributions for electron locations. According to this model, electrons do not move in precise orbits but are described by wave functions or orbitals that specify their spatial probability distribution. The quantum mechanical model takes into account the principles of quantum mechanics and the Heisenberg uncertainty principle.