The angular momentum of an electron by Bohr is given by mvr or nh/2π. According to Bohr’s atomic model, the angular momentum of electrons orbiting around the nucleus is quantized. Louis De Broglie further explained the quantisation of angular momentum.

When an electron in a hydrogen atom is in the first excited state, what prediction does the Bohr model give about its orbital speed and kinetic energy? What is the magnitude of its orbital angular momentum? Answer \(v_2 = 1.1 \times 10^6 m/s ≅0.0036 \, c;\) \(L_2 = 2\hbar K_2 = 3.4 \, eV\)

Bohr proposed that the allowed orbits are circular and must have quantized orbital angular momentum given by \[L = m_evr_n = n\dfrac{h}{2\pi} (n = 1, \, 2, \, 3, . . .), \nonumber\] where \(L\) is the angular momentum, \(r_n\) is the radius of the \(n\)th orbit, and \(h\) is Planck’s constant.

Bohr described angular momentum of the electron orbit as / while de Broglie's wavelength of = / described divided by the electron momentum. In 1913, however, Bohr justified his rule by appealing to the correspondence principle, without providing any sort of wave interpretation.

2021年3月24日 · During this stage Bohr was guided by experimental data of atoms being bombarded with high velocity electrons, and giving of characteristic x-rays. The data appeared to corroboratre an expected correlation between electron speed (in the lowest energy state), and the total charge of the nucleus.

Combining the energy of the classical electron orbit with the quantization of angular momentum, the Bohr approach yields expressions for the electron orbit radii and energies: Substitution for r gives the Bohr energies and radii:

2023年11月26日 · This page gives basic information about the Bohr model of the atom and the quantization of electron angular momentum. These concepts are the basis of modern quantum physics and thus are essential to master before progressing …

3 天之前 · The Bohr model states that the electrons in an atom make circular orbits around the nucleus. According to the Bohr model, electron angular momentum is quantized. This means that electron orbits are only possible where the angular momentum 𝐿 of an orbiting electron is an integer multiple of the reduced Planck constant ℏ: 𝐿 = 𝑛 ℏ.

Angular momentum is a conserved quantity (in a closed system) and this is true also for the angular momentum that is carried by the electromagnetic (EM) field. This conservation is a manifestation of rotational symmetry and the azimuthal part of …

Bohr’s proposal explained the hydrogen atom spectrum, the origin of the Rydberg formula, and the value of the Rydberg constant. Specifically it demonstrated that the integers in the Rydberg formula are a manifestation of quantization. The energy, the angular momentum, and the radius of the orbiting electron all are quantized.