Structure of Atom - Bohr Model

Study Notes

Bohr Model of the Atom

Electrons in the Bohr model occupy defined orbits, known as stationary states, which have fixed radii and energies.
Transitions between these states involve absorption or emission of radiation.
Angular momentum (l) of electrons is quantized, expressed as l = n h/2π, where h is Planck's constant and n is the principal quantum number.

Key Concepts

Stationary states define allowed energy levels for electrons characterized by the principal quantum number (n).
Principal quantum number (n) values (1, 2, 3...) correspond to increasing energy levels.
Electron orbit radius is given by r = _n_² a₀, where a₀ (Bohr radius) is 52.9 pm.
Energy in stationary states is represented by E = -R_h/_n_², with Rydberg's constant (R_h) being 2.18 × 10⁻¹⁸ J.
The ground state is the lowest energy state (n = 1), while excited states are any above this.

Energy and Stability

Negative energy indicates that an electron's energy is lower than that of a free electron.
Ground state (n = 1) is the most stable, corresponding to the most negative energy value.

Niels Bohr

Niels Bohr (1885-1962) was a Danish physicist known for his contributions to atomic theory.
He earned his Ph.D. from the University of Copenhagen and received the Nobel Prize in Physics in 1922.

Energy Level Diagram

Energy level diagrams illustrate different electron energy states within the hydrogen atom.
A free electron has zero energy; as n increases, the electron moves further from the nucleus, and energy levels become less negative.

Photon Emission in Hydrogen

Transition from n = 5 to n = 2 results in emission of a photon in the visible Balmer series.
Emission energy calculated as -4.58 × 10⁻¹⁹ J leads to frequency of 6.91 × 10¹⁴ Hz and wavelength of 434 nm.

Helium Ion (He⁺) Energy and Radius

The energy associated with He⁺ is calculated with E = (2.18 × 10⁻¹⁸ J)(Z²/n²), resulting in -8.72 × 10⁻¹⁸ J for Z = 2 and n = 1.
The radius for He⁺ calculated as r = (0.0529 nm)(n²/Z) gives 0.02645 nm.

Limitations of Bohr's Model

Bohr's model explains hydrogen's spectral lines, but fails to resolve finer details and cannot address the spectra of multi-electron atoms.
It cannot describe molecular formation or spectral line splitting due to external fields (Zeeman and Stark effects).

Advancements towards Quantum Mechanical Model

Dual nature of matter and the uncertainty principle led to a more holistic understanding of atomic structure.

Heisenberg Uncertainty Principle

States that the product of uncertainties in position (Δx) and momentum (Δp) is greater than or equal to h/4π.
Significant for microscopic particles; negligible for macroscopic objects.

Erwin Schrödinger

Austrian physicist who advanced quantum mechanics, notably through the Schrödinger equation, which describes wave-particle duality in atoms.
Shared the Nobel Prize for Physics with P.A.M. Dirac in 1933.

Quantum Mechanical Model

Replaces Bohr's model, accommodating the principles of wave-particle duality and uncertainty.
Quantized energy levels arise from the solutions to the Schrödinger equation.

Atomic Orbitals

Orbitals vary in size and shape, denoted by quantum numbers:
- Principal quantum number (n)
- Azimuthal quantum number (l)
- Magnetic orbital quantum number (m)

Principal Quantum Number (n)

Determines size and energy of orbitals.
Higher n corresponds to larger orbitals further from the nucleus.

Azimuthal Quantum Number (l)

Defines sub-shells and their characteristics.
l values correspond to shapes (s, p, d, f) of orbitals and increase with higher n.

Sub-shells

Number of sub-shells in a principal shell equals n value.
Each sub-shell is characterized by distinct quantum numbers and symbols.

Description

Explore the Bohr Model of the atom, which describes how electrons move in defined orbits around the nucleus. Learn about stationary states, quantized angular momentum, and the energy transitions that correspond to radiation absorption and emission. This quiz covers fundamental concepts of atomic structure based on Bohr's theory.