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The Bohr model is based on the quantum theory of radiation and the classical law of physics. Niels Bohr, 1913 proposed a theory combining the nuclear model of the atom with the quantum theory of light. On the basis of his thesis on the quantum theory of light on the intermittent, discrete nature of radiation and on the line nature of atomic spectra, he arrived at the conclusion that the energy states of an electron cannot change continuously, but the change in jumps discreetly. In other words, the energy states of the electrons in an atom are quantized.
Postulates of Bohr atomic model
An electron can revolve around a nucleus not in any arbitrary orbit but only in certain circular orbits.
The orbits are also known as stationary orbits.
Every orbit will have a definite amount of stable energy, and these orbits are called orbital shells. If in a stable orbital shell, electrons continuously rotate around the nucleus they do not emit energy.
Integers (such as n= 1, n=2, n=3) were used to denote different energy levels. And these integers are also called quantum numbers. Quantum numbers will be different for the smallest energy level and the highest energy level.
Energy levels orbits are considered in two different ways of devotion such as – 1,2,3,4 or K, L, M, N shells.
The radiation, either in the form of absorption or emission by the atom, takes place only when an electron jumps from the one stationary orbit of a certain energy level to another orbit of a different energy level.
hv = ∆ E
Where ‘h’ =Planck’s constant,
v = frequency of the radiant energy.
Hence, the spectrum of the atom will have a certain fixed frequency. Emission only occurs when an electron makes a jump (transition) from one stationary orbit to another. This is attained by the emission or absorption of a quantum of electromagnetic radiation whose energy levels equal the difference between the energy of the atom in the final and in the initial states. It will come to fall back to a lower energy orbit with the release of excess energy.
Stationary states or energy levels
In the Bohr model, the energy associated with the orbits around the nucleus is designated as energy levels. An electron must be from one of the permitted orbitals and have the appropriate energy required for that orbit to be in the electron-dense cloud of an atom. An electron would need less energy to orbit nearer to the nucleus, while an electron would need more energy to orbit farther from the nucleus.
Energy levels or stationary states refer to all of the potential orbits. We have different orbits in which electrons revolve around the orbits.
One of the flaws of the Bohr model is that it cannot explain why just particular energy levels or orbits are permitted. As per Bohr, electrons could only lose or gain energy by shifting from one energy level to another, acquiring or dropping precise quantities of energy.
Quantized energy levels indicate that only particular amounts are possible. It’d be like a stairwell, with only rungs at specific heights. The only way to get on the ladder would be to stand on one of the rungs. The only way to move up the ladder is to stand on one of the rungs up or down is to switch to another rung.
Assume we have a ladder with ten rungs. In the regular state, only one person can be on each level, and the ladder occupants must be on the lowest rung accessible. They would be on the bottom five rungs of the ladder if there were five persons on it. No one could move down in this case because all of the lower rungs are occupied.
In his model, Bohr devised restrictions for the most number of electrons that could be in each energy level, requiring that an atom in its normal state (ground state) have all electrons in the least energy state. We have different orbits in which electrons revolve around the orbits. No electron can decrease energy under these conditions because no electron can reach the least energy level. Bohr’s concept explained why electrons surrounding the nucleus did not emit energy and spiralled back into the nucleus in this fashion.
Bohr Model and Atomic Spectra
The atomic spectra provided evidence to back up Bohr’s theory. He proposed that the electrons in an atom move through energy levels to create an atomic spectrum. The ground state is the least energy state in which electrons can exist. The electrons in an atom can absorb energy by moving to a higher energy level, or excited state, if they are supplied with energy (via heat, electricity, light, or other means).
We have different orbits in which electrons revolve around the orbits. The electrons then release the energy they have received in the form of a photon, allowing them to return to a low energy state. Because the disparities in energy levels are accurate, the energy emitted by electrons falling to lower energy levels is always the precise quantity of energy.
When looking at an atomic spectrum, this explains why you see certain lines of light—each line belongs to a particular “step down” that an electron in that atom can take. This also explains why each element’s atomic spectrum is unique. Because each element’s electrons have various allowable energy levels, the electrons of each element can travel different paths than those of other elements.
The energy of an electron in Bohr’s Orbit
The energy ingested or discharged would reflect contrasts in the orbital energies as per this condition:
∆E = Ef – Ei = hv
In this situation, h is Planck’s constant, and Ei and Ef are the underlying and last orbital energies, individually. The outright worth of the energy contrast is utilized since frequencies are always positive. Rather than taking into account the nonstop upsides of energy, Bohr expected the energies of these electron orbitals were quantized:
En = -k/n², n=1, 2, 3, …
In this articulation, k is a steady containing essential constant, such as the electron mass and charge and Planck’s constant. Embedding the expression for the circle energies into the situation for ΔE gives, which is indistinguishable from the Rydberg condition in which R∞ = khc.
At the point when Bohr determined his hypothetical incentive for the Rydberg constant, R∞, and contrasted it and the tentatively acknowledged esteem, he got a magnificent understanding.
Since the Bohr model included just a solitary electron, it could likewise be applied to the single electron particles He+, Li2+, Be3+, etc, which contrast with hydrogen just in their atomic charges. Thus one-electron iotas and particles are aggregately alluded to as hydrogen-like molecules. The energy articulation for hydrogen-like molecules is a speculation of the hydrogen particle energy, where Z is the atomic charge (+1 for hydrogen, +2 for He, +3 for Li, etc.) and k has a worth of 2.179 × 10-18 J
En = -kZ²/n²
Advantages of Bohr’s Theory
Bohr’s theory clearly states the spectral lines pattern of single-electron species like Hydrogen, He+, Li2+, etc.
Uni-electron atoms will show the emission and absorption patterns at different levels of energy due to excitation.
Calculation of Radius of Bohr’s Orbit
According to Bohr, the radius of orbit in which electron moves is
r= (n²h²)/4π²me²Z
Where, n = Orbit number, m = Mass number; e = Charge on the electron
rₙ=0.529 n²/Z Ä
The quantization of energy of electron
1. In ground state: No energy emission. Value comes to 13.6eV
2. In excited state: Energy levels greater than n₁ are excited. i.e. for H- atom
n₂;n₃;n₄. etc. are excited states. For the H- atom the first excitation state is n₂.
3. Excitation potential: Energy required to excite electrons from the ground state to any excited state.
Ground state ⇒ Excited state
1st excitation potential = E₂ – E₁ == -3.4+13.6 =10.2 eV.
2nd excitation potential =
-1.5 +13 .6= 12 .1eV
4. Ionization energy: The minimum energy required to release the electron to the excited state.
effective ionization E ᵉⁿᵉʳᵍʸ = E+13.6 Z²/n² eV
5. Ionization potential: Vᶦᵒⁿᶦˢᵃᵗᶦᵒⁿ= Eᶦᵒⁿᶦˢᵃᵗᶦᵒⁿ/e
6. Separation energy: Energy required to excite an electron from an excited state to infinity:
SE = Eσ – Eexcited.
Limitations and Failures of the Bohr Model
Following are the limitations of the Bohr model:
When an electron returns to a lower energy state, it emits a relatively similar quantity of energy as radiation.
The existence of different lines in the H-spectrum was explained by Bohr Theory. However, it is expected that only a few lines exist. With the development of improved instruments and procedures, it was discovered that the spectral line that had been assumed to be a single line was a group of multiple lines that were quite similar (called fine spectrum). The individual Balmer series’ H spectral band, for example, is made up of numerous lines that are relatively close together.
As a result, the existence of many lines means that with every quantum number n, there exist several levels of energy that are near together. This would necessitate the creation of novel quantum numbers.
He could not give acceptable reasons for the supposition that the electron can cycle only in certain orbits in which the momentum of angular electron (MVC) is a multiple of a whole number of h/2𝜋, i.e. he could not give any reason for using the concept of quantization of angular momentum, which he invented randomly.
An electron in an atom, according to Bohr, is placed from the nucleus at a specific length and revolves around it with a constant velocity, i.e. it has a fixed amount of momentum. This goes against the Uncertainty Principle of Heisenberg, which states that determining a particle’s location and momentum concurrently with confidence is impossible.
Conclusion
The Bohr atomic model helps us to understand the hydrogen spectrum. The Bohr model of the atom was very successful in accounting for the main features of the hydrogen spectrum and the spectrum of singly ionized helium, single-electron species.
However, it failed to predict the energy states of more complicated systems containing more than one electron.
Some of the conclusions from the theory were found not to agree with observed facts.
The failure of Bohr’s theory led to the development of a new quantum mechanics, which remains our dominant worldview.
