Ch 7.1 and 7.2

Nature of Light

  • Light's properties are defined by frequency ($\nu$), wavelength ($\lambda$), and speed (c = $3.00 \times 10^{8}$ m/s).

  • Inverse relationship:λν=c.

  • Electromagnetic spectrum includes visible light (400 - 750 nm).

Characteristics of Waves

  • Wavelength ($\lambda$): distance between consecutive crests/troughs (units: meters, nm, Å).

  • Frequency ($\nu$): cycles per second (units: s$^{-1}$ or Hertz).

  • Amplitude: height of wave; can be positive/negative and affects intensity.

Interference of Waves

  • Superposition principle: multiple waves' amplitudes sum at a point.

  • Constructive interference: waves in phase; Destructive interference: waves out of phase.

Historical Development

  • Thomas Young's 1803 experiments showed light's wave nature (two-slit experiment).

  • Maxwell's equations (1873) describe classical electricity/magnetism.

  • Planck's quantum theory from blackbody radiation; $E = n h \nu$ introduced energy quantization.

  • Photoelectric effect (Einstein 1905): light behaves as photons, $E_{photon} = h \nu$.

Atomic Structure

  • Bohr model: electrons in quantized orbits; predicts discrete energy levels ($E = -\frac{m e^4}{8 \epsilon_0^{2} h^{2}} \frac{1}{n^2}$).

  • Rydberg equation for hydrogen's emission spectrum: $\frac{1}{\lambda} = RH (\frac{1}{n1^2} - \frac{1}{n_2^2})$. - Bohr model: Proposed by Niels Bohr in 1913, this model describes the behavior of electrons in hydrogen-like atoms. It posits that electrons orbit the nucleus in fixed, quantized orbits, rather than in continuous paths. These orbits are characterized by specific energy levels, represented mathematically as: E=−me48ϵ02h21n2E = -\frac{m e^4}{8 \epsilon_0^{2} h^{2}} \frac{1}{n^2} where $E$ is the energy of the electron, $m$ is the electron mass, $e$ is the elementary charge, $\epsilon_0$ is the permittivity of free space, and $h$ is Planck's constant. The variable $n$ is the principal quantum number which can take positive integer values (1, 2, 3,…). Each energy level corresponds to a specific orbit where the electron resides, and transitions between these levels result in the absorption or emission of electromagnetic radiation. - Rydberg equation for hydrogen's emission spectrum: The Rydberg formula provides a way to calculate the wavelengths of spectral lines in hydrogen. It is expressed as: 1λ=RH(1n12−1n22)\frac{1}{\lambda} = R_H \left(\frac{1}{n_1^2} - \frac{1}{n_2^2}\right) where $R_H$ is the Rydberg constant (approximately 1.097 times; 10^7 m^-1), $ u$ is the frequency, and $\lambda$ is the wavelength of the emitted or absorbed light. In this equation, $n_1$ and $n_2$ are integers representing the principal quantum numbers of the lower and higher energy levels, respectively. This equation reveals that the difference in energy between two levels dictates the wavelength of the emitted photon, thereby enabling the identification of distinct spectral lines corresponding to various electronic transitions in hydrogen.

  • Problems in the Bohr model included failure to predict multi-electron atoms and the effects of external magnetic fields.