Niels_Bohr_ ILLARIONOV VLADISLAV

1.

Key Terms
Quantization — Квантование
Stationary state — Стационарное состояние
Quantum transition — Квантовый переход
Wavefunction — Волновая функция
Energy eigenvalue — Собственное значение энергии
Reduced mass — Приведённая масса
Correspondence principle — Принцип соответствия
Complementarity principle — Принцип дополнительности
Wave-particle duality — Корпускулярно-волновой дуализм
Spectral series — Спектральная серия
Electromagnetic radiation — Электромагнитное излучение
Compound nucleus — Составное ядро
Nuclear fission — Деление ядра
Liquid-drop model — Капельная модель
Nuclear binding energy — Энергия связи ядра
Decay channel — Канал распада
Semi-empirical mass formula — Полуэмпирическая формула массы
Quantum measurement — Квантовое измерение
Dynamical instability — Динамическая неустойчивость
Quantum hypothesis — Квантовая гипотеза

2.

NIELS BOHR

3.

The transition from classical atomic models to quantum theory
Bohr’s 1913 atomic theory introduced discrete
stationary states and made atomic spectra a problem
of quantized energy differences rather than
continuous classical radiation.
He combined Rutherford’s nuclear atom with
Planck’s quantum hypothesis.
He introduced quantum jumps between stationary
states and the frequency condition hν = Ei − Ef.
His model quantitatively reproduced the hydrogen
spectrum and the ionization energy of hydrogen.
His correspondence principle became a bridge
between quantum and classical descriptions.
stationary states
energy quantization
spectroscopy

4.

Biography
1885
1911
1912
1913
1921
1922
1930s
1962
Born in Copenhagen
PhD: electron theory of
metals
Cambridge and
Manchester; Rutherford
Three papers “On the
Constitution of Atoms
and Molecules”
Institute for Theoretical
Physics opens
Nobel Prize in Physics
Nuclear structure and
compound nucleus
Dies in Copenhagen
He was born on October 7, 1885 in Copenhagen, DenmarkHe received
his early education from the Gammelholm Latin School which he joined
when he was seven. From 1903 he attended the Copenhagen University
where his major was physics, which he studied under Professor Christian
Christiansen.

5.

Academic formation and influences
Copenhagen
Training in mathematical physics
and electrodynamics. His PhD
analyzed the limitations of
classical electron theory in metals.
Cambridge
Worked near J. J. Thomson’s
research environment. Thomson’s
electron concept was central, but
Bohr did not find the classical
atomic picture satisfactory.
Manchester
Joined Ernest Rutherford, whose
scattering experiments implied a
compact positive nucleus. This
became the structural basis for
Bohr’s atom.
In 1909, he earned a master’s degree in physics and went on to complete his PhD in physics in 1911, both from the
University of Copenhagen. His doctoral dissertation was on the electron theory of metals. In 1911, he met J. J. Thompson
of the Cavendish Laboratory at the Cambridge University. He conducted some research on cathode rays, but failed to
impress Thomson. Later, Ernest Rutherford invited him to conduct post-doctoral research in England on the atomic
structures.
In 1913, Bohr’s paper on atomic structure was published which became the basis of the famous ‘old quantum theory’.
From 1914 to 1916, he worked as a lecturer of physics at the Victoria University of Manchester, UK.
In 1916, he became a professor of theoretical physics at the University of Copenhagen. He founded the ‘Institute of
Theoretical Physics’ at the Copenhagen University in 1920 and also served as its administrator until 1962.

6.

The classical crisis
For circular motion in a Coulomb field, classical mechanics gives a centripetal-force condition, but
classical electrodynamics predicts radiation from the accelerated charge.
μv² / r = Ze² / (4πε₀r²)
P ∝ a² → continuous energy loss
The left equation alone permits a continuum of orbital radii and energies.
The right-hand classical radiation result makes such an orbit dynamically unstable.
Bohr’s key move was to restrict the mechanically possible motions to a discrete set of
stationary states.
This was a semi-classical theory: classical equations of motion were retained, but quantum
conditions selected the allowed states.

7.

Bohr’s postulates (1913)
1. Stationary states
An electron may occupy certain allowed states without continuously
radiating electromagnetic energy, despite the classical expectation
for an accelerated charge.
2. Quantization condition
L = μvr = nħ, n = 1, 2, 3, …
This restricts the orbital angular momentum and therefore
discretizes the allowed radii and energies in the hydrogenic model.
3. Quantum transitions
hν = Ei − Ef
Emission or absorption occurs when the atom changes between
stationary states.

8.

Spectroscopy and the Rydberg relation
Johannes Rydberg had already found an empirical regularity for hydrogen spectral lines. Bohr’s theory
supplied a physical interpretation by deriving the same 1/n² structure from quantized atomic energies.
hν = Eᵢ − E_f
1/λ = R∞ Z² (1/n_f² − 1/n_i²)
Lyman series
Balmer series
Paschen series
n_f = 1 • ultraviolet
n_f = 2 • visible / near-UV
n_f = 3 • infrared
Scientific significance: spectroscopy became a direct probe of atomic energy-level structure.

9.

The correspondence principle
Bohr argued that quantum theory must reproduce the
predictions of classical physics in an appropriate limit —
especially for large quantum numbers and transitions
between neighboring levels.
n ≫ 1 ⇒ quantum predictions → classical behavior

10.

Complementarity and quantum measurement
In the late 1920s Bohr formulated the principle of complementarity: certain classical descriptions, such as
wave-like and particle-like accounts, are mutually exclusive in a given experimental arrangement but jointly
necessary for a complete account of quantum phenomena.
Wave description
Particle description
interference • diffraction • phase relations
localized detection • momentum transfer
counting events

11.

Nuclear physics: compound nucleus
Bohr proposed that many nuclear reactions proceed through an intermediate compound nucleus: the
incident particle is captured, its energy is redistributed among many nuclear degrees of freedom, and the
excited system later decays through an available channel.
excited
compound
nucleus
projectile
possible decay
channels
particle emission
γ-ray emission
fission, if energetically and dynamically accessible
Liquid-drop picture and fission
Bohr developed the liquid-drop analogy for the nucleus: short-range nuclear attraction favors a compact
drop, while Coulomb repulsion between protons and surface effects influence deformation and stability. This
picture became important in the early theory of nuclear fission.

12.

Key formulas and scientific vocabulary
Angular momentum
quantization
L = nħ
quantization condition
Bohr radius
a₀ = 4πε₀ħ²/(mₑe²)
characteristic hydrogen length scale
Hydrogenic radius
rₙ = a₀ n²/Z
allowed-radius scaling in the Bohr model
Energy levels
Eₙ = −13.6 Z²/n² eV
discrete bound-state energies (approx. infinite nuclear mass)
Bohr frequency condition
hν = Eᵢ − E_f
photon emission / absorption
Rydberg relation
1/λ = R Z²(1/n_f² − 1/n_i²)
spectral-series relation explained by Bohr theory

13.

Niels Bohr and Lev Landau

14.

In 1922, Bohr was awarded the Nobel Prize in Physics for his contributions to the study of the structure
of the atom. In his lecture "On the Structure of Atoms," delivered in Stockholm on December 11, 1922,
Bohr summarized his ten years of research.