Niels Bohr’s proposal of the Bohr’s model for hydrogen atom structure discovered in 1913. Rutherford’s atomic model had defect that Bohr fixed with a quantum-based model, especially when it came to atomic stability and spectral lines.
Bohr’s theory provided the first quantum explanation of atomic structure by using quantum mechanics to explain how electrons behave in atoms, especially when considering the simplest element, hydrogen.
Key Postulates of Bohr’s Model
Bohr’s model is based on the following key postulates:
1.Quantised Electron Orbits: Bohr asserts that electrons travel in different, well-defined orbits or energy levels around the nucleus, each of which has a fixed radius and energy.
Bohr suggested that there are only specific permitted orbits where electrons can live without emitting energy, in disparity to Rutherford’s concept. Atomic instability is addressed by these quantised orbits, which stop electrons from spiraling into the nucleus.
2. Angular Momentum Quantization: Bohr developed the idea of quantised angular momentum, which postulates that an electron’s angular momentum is limited to specific values. In particular, ℏ = h / 2π, where h is Planck’s constant, is an integer multiple of the angular momentum L of an electron in a certain orbit.
In mathematics, L = nℏ, where n is the primary quantum number, which is a positive integer. The number of potential orbits is effectively limited by this quantisation of angular momentum.
3. Energy Quantisation and Emission of Photons: A hydrogen atom’s electrons can only reside in specific energy levels. An electron absorbs or releases energy in the form of a photon when it moves between two energy levels.
The formula ΔE = E2 − E1 = hv, where ν is the photon’s frequency, represents the energy of the emitted or absorbed photon, which is the difference between the two energy levels. The line spectra of hydrogen and other elements can be explained by this energy quantisation.
Structure and Energy Levels
Each electron orbit in Bohr’s model represents a separate energy level, with the energy rising with the electron’s distance from the nucleus. The following formula can be used to determine the energy levels for the hydrogen atom:
En = − 13.6 eV / n2
where En is the energy of the n-th orbit, and n is the principal quantum number (1, 2, 3, …). The negative sign indicates that the electron is bound to the nucleus, with the lowest energy (ground state) at n = 1.
Bohr’s Model and Spectral Lines
The spectral lines seen in the emission spectrum of hydrogen were correctly described by Bohr’s hypothesis. A photon with an energy equal to the difference between the two energy levels is released when an electron in an excited state, which has a higher energy, moves to a lower energy level.
A spectral line is the result of this energy release. Electron transitions between particular orbits give rise to the various spectral lines found in hydrogen, including the Balmer and Lyman series.
Limitations of Bohr’s Model
It could not explain the spectra of atoms having more than one electron.
It does not satisfactorily explain the distribution of electrons in an atom.
It could not explain the spitting of spectral lines under the influence of magnetic field (Zeeman effect) and electric field (Stark effect).
Dual nature of particle and the uncertainty principle was ignored in the Bohr’s model.
Impact :-
Bohr’s model established the groundwork for contemporary quantum mechanics, in spite of its drawbacks. It offered a framework for understanding atomic structure and introduced quantisation concept.
Bohr’s theories were later developed further by more sophisticated theories like Schrödinger’s wave mechanics, which integrated quantum principles to offer a more thorough explanation of atomic and subatomic particles.
A pivotal moment in atomic theory, Bohr’s model of the hydrogen atom captures the development and transitory character of early quantum mechanics.
Note :-
The electron in a hydrogen atom move around nucleus in certain path, of fixed radius and energy, called orbits or energy shells.
Energy of electron does not change with time.
However, when electron moves from lower to higher energy shell, it absorbs energy and energy releases when it come back.
Bohr’s model, which describes electron orbits as distinct energy levels, is based on quantum theory and describes the hydrogen atom. According to this hypothesis, electrons only emit or absorb energy when they move between orbits around the nucleus; they do not lose energy while doing so.
By suggesting that electrons occupy fixed orbits with particular energy levels, Bohr’s model resolves the stability problem by stopping them from endlessly emitting energy and spiraling into the nucleus.
An electron can move in quantized orbits, which have defined, set energy levels, without releasing energy. Until they shift to a new orbit, electrons in these orbits keep their energy constant.
According to Bohr, electron transitions between orbits produce spectral lines. Spectral lines are produced when an electron falls to a lower energy orbit and releases a photon with an energy equal to the difference between the two levels.
Only single-electron atoms, such as hydrogen, are adequately described by Bohr’s model. Because it ignores electron-electron interactions and does not explain spectral line fine structures, it is ineffective for multi-electron atoms.
With n as the principal quantum number, the energy of the n-th orbit in Bohr’s hydrogen atom model is given by En = −13.6 eV / n2. The fact that electrons exclusively inhabit particular energy levels is explained by this quantisation.