Quantum levels of the atom

Содержание и основные понятия

In the Bora model, the electron in the hydrogen atom has permitted fixed states and emits only between them. The model explains the spectrum of hydrogen, but gives way to quantum mechanics for complex atoms.
GEF · 11 grade
PIF · Baseline
Interactive model
Hospitality
Core level
excitation
ionization
01
The physical picture
What happens and what boundaries the model has.
Main message
In the Bora model, the electron in the hydrogen atom has permitted fixed states and emits only between them. The model explains the spectrum of hydrogen, but gives way to quantum mechanics for complex atoms.
In fixed orbit, the electron does not emit as part of a postulate.
The absorption is moving the atom to a higher level.
Ionization corresponds to electron withdrawal into a continuous range of states.
How to reason
First, name the system and the interaction, then select the values, and only then write down the law. The formula works within the model's assumptions.
02
Laws and values
Symbols should be read as a relationship of values, not as a recipe for substitution.
E
n
=
−
13.6
n
2
e
V
E_n=-\frac{13.6}{n^2}\,\mathrm{eV}
E
n
​
=
−
n
2
13.6
​
eV
Energy levels of hydrogen atom
h
ν
=
∣
Δ
E
∣
h\nu=|\Delta E|
h
ν
=
∣Δ
E
∣
Quantum energy at transition
Review of the situation
The transition to a lower level is accompanied by a photon whose energy is exactly equal to the different levels.
04
Links and application
In the real world
The transition to a lower level is accompanied by a photon whose energy is exactly equal to the different levels.
Model verification
Compare the prediction with observation, evaluate the units, the order of magnitude and the influence of the factors not taken into account. Disparity does not always mean an error of law: often idealization is no longer sufficient.
C
What needs to be understood
Outcome 1
Explain the physical meaning of the topic "Quantum levels of the atom" through the model, not just the formula.
Outcome 2
Distinguish and correctly use terms: state of residence, basic level, excitation.
Outcome 3
Indicate the conditions for the applicability of the law, verify units and limit cases.
T
Terms of the topic
The definition should indicate the physical meaning, not a substitute for a domestic synonym.
Hospitality
Quantum state with a certain energy that doesn't change over time without external influence.
Core level
Quantum system status with the lowest possible energy.
excitation
The transformation of the atom or other quantum system into a state of greater energy.
ionization
The formation of charged particles from neutral atoms or molecules when the electrons are lost or joined.
F
Origin and conclusion of the formulas
The fundamental law cannot be "proven" by algebras: for each record, it is stated whether it is a definition, an experimental law, or a model effect.
E
n
=
−
13.6
n
2
e
V
E_n=-\frac{13.6}{n^2}\,\mathrm{eV}
E
n
​
=
−
n
2
13.6
​
eV
model effect
Hydrogen levels.
The following is an indication of the definition, experience or law from which this entry arises and where it is applicable.
m
v
2
r
=
e
2
4
π
ε
0
r
2
\frac{mv^2}{r}=\frac{e^2}{4\pi\varepsilon_0r^2}
r
m
v
2
​
=
4
π
ε
0
​
r
2
e
2
​
In the Bora model, the Culon force holds the electrons in circular orbit.
m
v
r
=
n
ℏ
mvr=n\hbar
m
v
r
=
n
ℏ
Only individual orbits are allowed by the quantization of the pulse moment.
E
n
=
K
+
U
=
−
m
e
e
4
2
(
4
π
ε
0
)
2
ℏ
2
n
2
=
−
13.6
n
2
e
V
E_n=K+U=-\frac{m_e e^4}{2(4\pi\varepsilon_0)^2\hbar^2n^2}=-\frac{13.6}{n^2}\,\mathrm{eV}
E
n
​
=
K
+
U
=
−
2
(
4
π
ε
0
​
)
2
ℏ
2
n
2
m
e
​
e
4
​
=
−
n
2
13.6
​
eV
The co-decision and sum of kinetic with potential energy provide discrete levels.
Conditions:
Non-relativist isolated hydrogen atom in the Bor model, fixed point core; n = 1, 2, ..., zero energy corresponds to free electron.
Monitoring:
The dimensions of both parts shall coincide; the result shall be checked for sign, order and limit case.
h
ν
=
∣
Δ
E
∣
h\nu=|\Delta E|
h
ν
=
∣Δ
E
∣
Postulate or Model
Quantum of transition.
The following is an indication of the definition, experience or law from which this entry arises and where it is applicable.
Δ
E
=
E
кон
−
E
нач
\Delta E=E_{\text{кон}}-E_{\text{нач}}
Δ
E
=
E
Cot
​
−
E
start
​
The transition between fixed levels changes the energy of the atom to ΔE.
E
γ
=
h
ν
E_\gamma=h\nu
E
γ
​
=
h
ν
The photon absorbed or emitted has a positive energy h.
E
γ
=
∣
Δ
E
∣
⇒
h
ν
=
∣
Δ
E
∣
E_\gamma=|\Delta E|\quad\Rightarrow\quad h\nu=|\Delta E|
E
γ
​
=
∣Δ
E
∣
⇒
h
ν
=
∣Δ
E
∣
The energy storage connects the Quantum frequency to the level differential module.
Conditions:
The one-phototon transition between fixed levels of the atom; the impact and external disturbance of the levels are neglected.
Monitoring:
The dimensions of both parts shall coincide; the result shall be checked for sign, order and limit case.
!
Model boundaries and typical errors
Error: Forget model condition
You can't transfer the formula to any situation just because it's a coincidence of letters. The key condition of this topic is that an electron does not emit in a fixed orbit within a postulate.
How to Check the Mind
The absorption translates the atom to a higher level. Then check the units, vector direction, and behavior of the result at zero or very large parameter.
Σ
Conclusion on the topic
Quantum levels of the atom
In the Bora model, the electron in the hydrogen atom has permitted fixed states and emits only between them. The model explains the spectrum of hydrogen, but gives way to quantum mechanics for complex atoms.
In fixed orbit, the electron does not emit as part of a postulate.
The absorption is moving the atom to a higher level.
Any numerical result shall be accompanied by a unit, a sign and an explanation of its physical meaning.
The content is consistent with the FRP on Physics of the OS/OSS 2025 and the subject matter of the current lines of the PNP: I. M. Peryškin and co-authors (7–9), G. J. Mäkishev and coauthors (10–11), and with the lines "Engineers of the Future" and V. A. Kasyanov. The original texts are not reproduced, the text of the textbooks is not reproduced.