Chemistry Lecture 3 Exam

Properties of Waves

• Wavelength (λ) is the distance between identical points on successive waves.

• Amplitude is the vertical distance from the midline of a wave to the peak or
  trough.

• Frequency (v) is the number of waves that pass through a particular point in

  • 1 second (Hz = 1 cycle/s).

  • The speed (u) of the wave = λ x v

Light as a Wave

• Maxwell (1873), proposed that visible light consists of electromagnetic waves

• Electromagnetic radiation is theemission and transmission of energy in the form of
  electromagnetic waves.

• All electromagnetic radiation travels at the same velocity:

  • Speed of light (c) = 3.00x10^8 m/s3

  • Wavelength (λ) and frequency (v) are related using

    • C = λV

Electromagnetic Spectrum

Quantized Energy and Photons

• Three observed properties associated with how atoms interact with electromagnetic radiation cannot be explained by waves:
  1) The emission of light from hot objects (blackbody radiation)
  2) The emission of electrons from metal surfaces on which light is shone (the photoelectric effect)
  3) Emission of light from electronically excited gas atoms (emission spectra)

Quantized Energy

• Max Planck explained energy by assuming that energy comes in packets called quanta (singular: quantum).

• Think of stairs (quanta) versus a ramp (continuous).

Mystery #1, “Heated Solids Problem” Solved by Planck in 1900

• When solids are heated, they emit electromagnetic radiation over a wide range of wavelengths.

• Radiant energy emitted by an object at a certain temperature depends on its wavelength.

• Energy (light) is emitted or absorbed in discrete units
  (quantum).

Mystery #2, “Photoelectric Effect” Solved by Einstein in 1905

Light has both:
1. wave nature
2. particle nature

Photon is a “particle” of lighth KE W
hv = KE + W

KE = hv - W
- where W is the work function and depends how strongly electrons are held in the
metal.

The Photoelectric Effect

• Einstein used quanta to explain the photoelectric effect.

• Each metal has a different energy at which it ejects electrons.

• At lower energy, electrons are not emitted

• He concluded that energy is proportional to frequency:

  • E = hv

  • where h is Planck’s constant 6.626 × 10^-34 Jxs

Atomic Emission of Gas

• Another mystery in the early twentieth century involved the emission spectra observed from energy emitted by atoms and molecules.

Atomic Spectrum

• When light from a heated element passes through a prism, it separates into distinct lines of color separated by dark areas called an atomic spectrum.
  
  

Line Spectra and the Bohr Model

• For atoms and molecules, one does not observe a continuous spectrum (the “rainbow”), as one gets from a white light source passed through a prism

• Only a line spectrum of discrete wavelengths is observed.

• Each element has a unique line spectrum

Electron Energy Levels

• The lines in an atomic spectrum are associated withmthe changes in energies of the electrons.

• In an atom, each electron has a specific energy, known as its energy level, which

• is assigned principal quantum numbers (n) = (n = 1,
  n = 2, …).

• increases in energy as the value of n increases and
  as electrons are farther away from the nucleus.

• The energy of an electron is quantized—electrons can have only specific energy values.

Electrons and Energy Levels

• Electrons with the same energy are grouped in the same energy level.

• Energy levels are assigned values called principal quantum numbers (n), (n = 1, n = 2, …).

• n increases, as energy increases (farther away from nucleus)

Changes in Electron Energy Level

• Electrons move to a higher energy level when they absorb energy.

• When electrons fall back to a lower energy level, Light is emitted

• The energy emitted or absorbed = differences between the two energy levels.

The Hydrogen Spectrum

• Johann Balmer (1885) discovered a simple formula relating the four emission lines to integers.

Bohr’s Model of the Atom (1913)

• e- can only have specific (quantized) energy values

• light is emitted as e- moves from one energy level to a lower energy level

The Bohr Model

• Niels Bohr adopted Planck’s assumption and explained
  these phenomena in this way:

• 1) Only orbits of certain radii, corresponding to specific energies, are permitted for the electron in a hydrogen atom.

• 2) An electron in a permitted orbit is in an “allowed” energy state. An electron in an allowed energy state does not radiate energy, and, therefore, does not spiral into the nucleus.
  3) Energy is emitted or absorbed by the electron only as the electron changes from one energy state to another. This energy is emitter of absorbed as a photon that has energy

  • E=hv

  • h = Planck constant 6.626 × 10^-34 Jxs

• Electrons in the lowest energy state are in the ground state, n= 1.

• Any energy higher is called an excited state, , n > 1. Since each orbit has a specific value compared to, HR transitions from one energy level to another can be calculated:

Energy State Values

• What do the values mean using the Bohr Model?

• A positive E means energy is absorbed. A photon is absorbed in this instance.

  • This happens if nf>ni

• A negative E means energy is released. A photon is emitted
  in this instance.

  • This happens if nf<ni

Energy Transitions of the Hydrogen Atom

Limitations of the Bohr Model

• This model only works for hydrogen (one electron).
  1. Classical physics would result in an electron falling into the positively charged nucleus. Bohr simply assumed it would not.
  2. Electrons have wave-like properties that must be accommodated.

Important Ideas from the Bohr Model

• Points that are incorporated into the current atomic model include the following:
  1) Electrons exist only in certain discrete energy levels, which are described by quantum numbers.
  2) Energy is involved in the transition of an electron from one level to another.

The Wave Behavior of Matter

• Louis de Broglie theorized that if light can have material properties, matter should exhibit wave properties.

• He demonstrated that the relationship between mass and wavelength was:

Quantization of Electron Energy

• Why is e- energy quantized?

• De Broglie (1924) reasoned that e- is both particle and wave.

Heisenberg Uncertainty Principle

• How do find a particle that acts like a wave?

• Heisenberg uncertainty principle – it is impossible to know simultaneously both the momentum, p (defined as mass times velocity) and the position of a particle with certainty.

The Uncertainty Principle

• Heisenberg proposed the dual nature of matter (particle and wave).

• He showed that the more precisely the momentum of a particle is known, the less precisely its position is known: