Ch. 18 Spectrophotometry I

This set covers fundamental concepts of spectrophotometry, including wave properties, electromagnetic interaction with matter, Beer's Law, and calibration methods based on Lecture 15 notes.

Amplitude ($A$)

The height of a wave, measured from the node to the crest, which serves as a measure of intensity; higher amplitude corresponds to brighter light.

Wavelength ($\lambda$)

The physical distance from one crest of a wave to the next.

Frequency ($\nu$)

The number of waves that pass a given point in a given amount of time.

Speed of light ($c$)

The velocity at which electromagnetic radiation travels, valued at $3 \times 10^8\,m/s$.

Wavenumber ($\tilde{\nu}$)

The reciprocal of wavelength, specifically $1/\lambda$, where $1\,cm^{-1} = \frac{10000}{\lambda\,(\mu m)}$.

Spectroscopy (Spectrophotometry)

The study of the interaction between light and matter.

X-ray

A type of high-energy radiation that interacts with atoms or molecules by removing electrons.

Ultraviolet-Visible (UV-Vis) radiation

Wavelengths that promote electrons to higher energy levels (atomic or molecular orbitals) and are associated with electronic transitions.

Infrared (IR) radiation

Radiation that interacts with molecules only, specifically by causing bond vibrations.

Microwave radiation

Low-energy radiation that interacts with molecules by causing molecular rotation.

Ground state

The lowest energy state of an atom or molecule.

Excited state

A higher energy state of an atom or molecule achieved after absorbing energy.

Quantized energy levels

The concept that energy levels in an atom are discrete, meaning absorbance only occurs if the energy of the photon ($E_{photon} = h\nu$) exactly matches the difference between energy levels ($\Delta E_{atom}$).

Fraunhofer lines

Prominent absorption lines in the solar spectrum, often associated with elements like Sodium (Na), Hydrogen (H), Calcium (Ca), Magnesium (Mg), and Neon (Ne).

Schematic diagram

Also known as a "box" diagram, it represents the parts of an instrument in their correct functional order rather than Providing a photographic likeness.

Beer-Lambert Law (Beer's Law)

The linear relationship between absorbance and concentration, defined by the equation $A = \varepsilon bc$.

Molar absorptivity ($\varepsilon$)

The probability that a photon will be absorbed by a sample, with units expressed as $L/(mol \cdot cm)$.

Path length ($b$)

The distance light travels through a sample, measured in units of $cm$.

Transmittance ($T$)

The fraction of light that passes through a sample, defined by the ratio $T = \frac{P}{P_0}$.

Absorbance ($A$)

A measure of light absorption calculated as $A = -\log T$ or $A = -\log(\frac{P}{P_0})$; for example, $A = 1$ indicates that $10\%$ of light is transmitted.

Linear region

The range on a calibration curve where absorbance varies linearly with concentration; at very high concentrations, molecular interactions cause the curve to become non-linear.

Absorption spectrum

A plot of absorbance ($A$) as a function of wavelength ($\lambda$).