2/13 Chem electromagnetic energy and the Bohr model of the atom

Metal Ion Flame Test Colours

Metal Ions and Flame Test Colours:
- Lithium (Li0): Characteristic flame colour.
- Sodium (Na+): Characteristic flame colour.
- Potassium (K+): Characteristic flame colour.
- Rubidium (Rb+): Characteristic flame colour.
- Caesium (Cs+): Characteristic flame colour.
- Calcium (Ca2+): Characteristic flame colour.
- Strontium (Sr²+): Characteristic flame colour.
- Barium (Ba²+): Characteristic flame colour.
- Radium (Ra²+): Characteristic flame colour.
- Copper (Cu²+): Characteristic flame colour.
- Iron (Fe²+/Fe³+): Characteristic flame colour.
- Boron (B3+): Characteristic flame colour.
- Indium (In³+): Characteristic flame colour.
- Lead (Pb2+): Characteristic flame colour.
- Arsenic (As³+): Characteristic flame colour.
- Antimony (Sb³+/Sb⁵+): Characteristic flame colour.
- Selenium (Se²/Se*+): Characteristic flame colour.
- Zinc (Zn²+): Characteristic flame colour.

Note: The metal ions shown on the bottom row have flame colours that are faint and difficult to distinguish.
Flame Test Procedure:
A flame test is an analytical procedure used by chemists to detect the presence of particular metal ions, based on the colour of the flame produced.
Mechanism:
When heated, the electrons in the metal ion gain energy, causing them to move to higher energy levels.
Due to energetic instability, electrons will tend to fall back to their original energy levels, releasing energy.
This energy is released in the form of light.
Conclusion: Different metal ions produce characteristic colours due to varying energy level differences.

Electromagnetic Energy and the Bohr Model of the Atom

Wave Properties

Definition of a Wave:
- A wave is described as an oscillation or periodic movement, capable of transporting energy from one point in space to another.
Characteristics of Waves:
- Wavelength (BB):
- Definition: The distance between two consecutive crests (peaks) or troughs in a wave.
- Frequency (6):
- Definition: The rate of oscillation—how many wave cycles pass a stationary point per second.
- Unit: Expressed as cycles per second (s2) or hertz (Hz).
- Amplitude:
- Definition: Half of the distance between the peaks and troughs of a wave.

Electromagnetic Radiation

Electromagnetic Spectrum:
- Definition: The entire range of all types of electromagnetic radiation.
- Speed of Light (c):
- Electromagnetic waves can travel through a vacuum at a constant speed, known as the speed of light.
- Wave Equation:
- The product of wavelength and frequency equals the speed of the wave:
  c = BB
  u where c = 2.998 imes 10^8 ext{ m/s}.

Particle Nature of Light

Photon:
- Definition: Light energy is not continuous; it exists in discrete packets called quanta. A photon represents one quantum of electromagnetic radiation.
- Photon Energy:
- The energy of a photon is dependent on its frequency:
  E = h
  u where h = 6.626 imes 10^{-34} ext{ J s} (Planck’s constant).

Energy Relationships

Energy Calculation for One Photon:
- The energy can also be expressed as:
  E = h
  u
Relationships:
- Using the definitions:
- u = c/BB
- Therefore, E = h c /BB.
Constants:
- h = 6.63 imes 10^{-34} ext{ J s}
- Since c = 2.998 imes 10^8 ext{ m/s}, this forms the basis for other calculations.

Example Calculations

Frequency Calculation:
- Question: What is the frequency, in Hz, of electromagnetic radiation that has a wavelength of 530.0 nm?
- Given formula: c = BB
  u
- Rearranging gives
  u = c/BB
- u = (2.998 imes 10^8 ext{ m/s}) / (5.30 imes 10^{-7} ext{ m}) = 5.66 imes 10^{14} ext{ s}^{-1}.
Energy Calculation:
- Calculate the energy, in kilojoules, of one mole of photons of red light (wavelength 632.8 nm).
- Energy of one photon:
  E_{photon} = rac{hc}{BB} = (6.63 imes 10^{-34} ext{ J s})(3.0 imes 10^8 ext{ m/s}) / (6.328 imes 10^{-7} ext{ m}) = 3.14 imes 10^{-19} ext{ J}.
- Energy for one mole:
  E = E{photon} imes NA where N_A = 6.022 imes 10^{23} ext{ photons/mol}
  E = 3.14 imes 10^{-19} ext{ J} imes 6.022 imes 10^{23} ext{ photons} = 1.89 imes 10^5 ext{ J} = 1.89 imes 10^{2} ext{ kJ}

Photoelectric Effect

Experimentation:
- When light of a specific wavelength is directed at the surface of a metal, it may cause the emission of electrons if the light has sufficient energy.
Dual Nature of Light:
- This phenomenon illustrates the wave-particle duality of light, indicating that electromagnetic radiation exhibits both wave behavior (characteristic by wavelength and frequency) and particle behavior (as photons with quantifiable amounts of energy).
Key Equation:
- The energy can be expressed as:
  E = h
  u = rac{hc}{BB}

Historical Context of Atomic Theories

Evolution of Atomic Models:
- Discussion on historical atomic models:
- Solid Sphere Model (John Dalton, 1803):
  - Atoms are indivisible and identical within an element.
- Plum Pudding Model (J.J. Thomson, 1904):
  - Proposed the existence of electrons as 'corpuscles' within a positively charged cloud.
- Nuclear Model (Ernest Rutherford, 1911):
  - Demonstrated that atoms have a nucleus; positive charge concentrated within it.
- Planetary Model (Niels Bohr, 1913):
  - Proposed that electrons exist in quantized orbits around the nucleus, addressing the emission spectra but not accounting for heavier atoms.

The Bohr Model of the Hydrogen Atom

Bohr's Model:
- Electrons move around the nucleus only in specific circular orbits with set (allowed) energies.
- An atom does not emit energy while an electron remains in one of these orbits.
- To change orbits, an electron must absorb or emit a photon with energy equal to the energy difference between these levels.
Energy Levels:
- Each orbit represents a specific, calculable energy level, with the ground state at n = 1.
- As n increases:
- The average distance of the electron from the nucleus increases.
- The energy levels become closer together.
- The orbits spread farther apart.

Absorption and Emission Processes

Absorption:
- An electron absorbs a photon, moving from a lower energy level to a higher one (
- Transition shown as: nf > ni).
Emission:
- An electron moves down from a higher energy level to a lower one, emitting a photon (transition shown as: ni > nf).
Color Determination:
- The energy difference between levels determines the color (wavelength) of light emitted.
- The specific energy change can be described by:
  riangle E = h
  u.

Spectroscopy

Continuous vs. Line Spectrum:
- Continuous Spectrum: An unbroken series of wavelengths.
- Line Spectrum: Narrow lines representing specific wavelengths of light emitted.

Line Spectra Details

Emission Lines:
- Each line signifies a distinct wavelength of light emitted, showing that the gas emits a set of discrete energies.
- Represented by the equation:
  E_{photon} = h
  u = rac{hc}{BB}.

Transitions in Energy Levels

Energy Transition Changes:
- Absorption: riangle E is positive.
- Emission: riangle E is negative.
- Energy of a photon correlates to the absolute value of riangle E.
Energy Levels:
riangle E = E{final} - E{initial} = -2.18 imes 10^{-18} ext{ J} igg( rac{1}{nf^2} - rac{1}{ni^2} igg).

Emission Spectra of Hydrogen

Line Spectrum:
- Visible lines occur when an electron transitions from a higher energy level to n = 2, emitting photons corresponding to specific wavelengths.
- Key transitions include:
- n = 6 → n = 2
- n = 3 → n = 2
- n = 4 → n = 2
- n = 5 → n = 2

Contributions and Shortcomings of Bohr's Model

Contributions:
- Electrons are quantized in fixed energy levels.
- Electrons can transition between energy levels by absorbing or emitting energy.
Shortcomings:
- Only accurately explains hydrogen's emission spectrum.
- Assumes circular electron orbits.
- Fails to incorporate the wave nature of electrons, indicating modern quantum models are required.