Electromagnetic Spectrum and Line Spectra

Electromagnetic Spectrum

The electromagnetic spectrum is the range of all types of electromagnetic radiation. It includes radio waves, microwaves, infrared radiation, visible light, ultraviolet radiation, X-rays, and gamma rays.

Equations

Wavelength to frequency

The frequency of an electromagnetic wave is directly proportional to its wavelength, and inversely proportional to the speed of light.

$f = \frac cλ$

Where:

• $f$ is the frequency of the wave, measured in Hertz (Hz)
• $c$ is the speed of light, measured in meters per second (m/s)
• $λ$ is the wavelength of the wave, measured in meters (m)

Wavelength to energy

The energy of an electromagnetic wave is directly proportional to its frequency, and inversely proportional to its wavelength.

$E = h \times f$

Where:

• $f$ is the frequency of the wave, measured in Hertz (Hz)
• $E$ is the energy of the wave, measured in joules (J)
• $h$ is Planck’s constant, measured in joule-seconds (J·s)

Constants

Speed of light

The speed of light is a fundamental constant in physics, and is defined as the speed at which electromagnetic waves propagate in a vacuum.

$c = 299,792,458 \space ms^{-1}$

Planck’s constant

Planck’s constant is a fundamental constant in quantum mechanics, and relates the energy of a photon to its frequency.

$h = 6.626 \times 10^{-34} \space Js$

Line Spectra

Role of Elections and Photons

• Electrons can be found in different energy levels within an atom.
• When an electron jumps from a higher energy level to a lower one, it releases energy in the form of a photon.
• The electron jumps up to a higher energy level, when when absorbs energy in the form of a photon.
• The energy of the photon determines its wavelength and color.
• The behavior of electrons and photons is fundamental to understanding line spectra.

Emissions

• Emissions occur when an electron releases energy in the form of a photon.
• The resulting line spectra can be used to identify the elements in a sample.
• The number and spacing of the lines are unique to each element.

Absorption

• Absorption occurs when an electron absorbs energy in the form of a photon.
• The energy can cause the electron to jump to a higher energy level.
• When the electron falls back down, it releases a photon with the same energy and wavelength as the absorbed photon.

Lyman

• The Lyman series is a set of emission lines in the ultraviolet region of the spectrum.
• These lines are caused by electrons transitioning to the n=1 energy level.
• The lines are closely spaced and become more closely spaced as they move towards shorter wavelengths.

Balmer

• The Balmer series is a set of emission lines in the visible and near-ultraviolet regions of the spectrum.
• These lines are caused by electrons transitioning to the n=2 energy level.
• The lines are more widely spaced than the Lyman series.

Paschen

• The Paschen series is a set of emission lines in the infrared region of the spectrum.
• These lines are caused by electrons transitioning to the n=3 energy level.
• The lines are even more widely spaced than the Balmer series.

By understanding the behavior of electrons and photons, we can interpret line spectra and identify the elements present in a sample.

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