One reason carbon monoxide (CO) is toxic is that it binds to...

One reason carbon monoxide (CO) is toxic is that it binds to the blood protein hemoglobin more strongly than oxygen does. The bond between hemoglobin and CO absorbs radiation of $1953 \mathrm{~cm}^{-1}$. (The unit is the reciprocal of the wavelength in centimeters.) Calculate the wavelength (in $\mathrm{nm}$ and $\dot{\mathrm{A}}$ ) and the frequency (in $\mathrm{Hz}$ ) of the absorbed radiation.

Key Concepts

Electromagnetic Radiation

Electromagnetic radiation is energy that travels in waves and spans a spectrum of wavelengths and frequencies. It is characterized by its speed, which in a vacuum is constant, and its properties such as wavelength, frequency, and energy. Understanding electromagnetic radiation is key to interpreting how light interacts with matter and is central to many areas of physics and chemistry, including spectroscopy.

Wavenumber

Wavenumber is a measure used in spectroscopy that represents the number of wave cycles per unit distance, typically per centimeter. It is the inverse of the wavelength expressed in centimeters and provides a convenient way to describe the position of spectral lines. A higher wavenumber corresponds to a shorter wavelength and higher energy photon.

Wavelength

Wavelength is the distance between successive crests or troughs of a wave and is an intrinsic property of electromagnetic radiation. It determines the classification of radiation within the electromagnetic spectrum and can be related to the wavenumber by taking its inverse. Accurate conversion between different units of wavelength, such as centimeters, nanometers, and Angstroms, is crucial for comparing measurements across various scientific disciplines.

Frequency

Frequency refers to the number of cycles of a wave that pass a given point per unit time. In the context of electromagnetic radiation, frequency is directly proportional to the energy of the radiation. The relationship between frequency, wavelength, and the speed of light is fundamental; it is given by the formula frequency equals the speed of light divided by the wavelength, an equation that forms the basis for many analyses in spectroscopy.

Unit Conversion

Unit conversion is the process of converting a measurement from one unit to another. In the context of electromagnetic radiation, it often involves converting between units such as centimeters, nanometers, and Angstroms for wavelength. Mastery of unit conversion is critical for ensuring that calculations are consistent and accurate across different systems of measurement in scientific problems.

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