EM Radiation & Planck's Quantum Theory

Master the relationships between wavelength, frequency, and photon energy.

8 lessons

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Wave Nature of Light

Introduce Maxwell's EM waves, frequency, wavelength, and wavenumber.

Wave Nature of Light

In the 1870s, James Clerk Maxwell revealed that when electrically charged particles accelerate, they produce alternating electrical and magnetic fields.

These fields transmit through space as electromagnetic waves (or electromagnetic radiation). Unlike sound waves, electromagnetic waves do not require a physical medium to travel—they can pass through a perfect vacuum.

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EM Radiation & Planck's Quantum Theory Visual

An image showing the EM wave components and the EM spectrum is crucial for visualizing frequency vs wavelength.

Clean scientific diagram of an electromagnetic wave showing oscillating electric and magnetic fields perpendicular to ea…

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Wave Equation

Formula card for c = nu * lambda.

The Wave Equation

c = ν λ

Where:

$c$ = Speed of light ( $3.0 \times 1 0^{8} m/s$ )
$ν$ = Frequency ( $Hz$ or $s^{- 1}$ )
$λ$ = Wavelength ( $m$ )

Wavenumber Formula

\overline{ν} = \frac{1}{λ}

Wavenumber ( $\overline{ν}$ ) is the number of wavelengths per unit length (typically $cm^{- 1}$ or $m^{- 1}$ ).

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Worked Example: Broadcasting Frequencies

Calculate wavelength from frequency.

Problem. The Vividh Bharati station of All India Radio broadcasts on a frequency of $1368 \text{ kHz}$ (kilo hertz). Calculate the wavelength of the electromagnetic radiation emitted by the transmitter. Which part of the electromagnetic spectrum does it belong to?

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Faded Example: Wavenumber and Frequency

Calculate wavenumber and frequency from wavelength in Angstroms.

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In Problem 2.5, we calculate the wavenumber and frequency of yellow radiation having a wavelength of $5800 \text{ \AA}$ . First, convert the wavelength into standard SI units. Since one Angstrom is $10^{-10} \text{ m}$ , we express the wavelength as $\lambda = 5800 \times$ m. The wavenumber ( $\overline{\nu}$ ) is the number of wavelengths per unit length, defined as $\overline{\nu} = 1/\lambda$ . Substituting our value gives $\overline{\nu} = 1 / (5800 \times 10^{-10} \text{ m})$ , which equals $\text{m}^{-1}$ . Next, we calculate the frequency ( $\nu$ ) using the equation $\nu = c/\lambda$ . Using the speed of light $c = 3 \times 10^8 \text{ m s}^{-1}$ , the division yields a frequency of $\text{s}^{-1}$ . This procedural approach ensures unit consistency across all electromagnetic spectrum calculations.

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Particle Nature: Planck's Quantum Theory

Introduce quanta and Planck's equation.

Particle Nature: Planck's Quantum Theory

While the wave nature of light elegantly explained phenomena like diffraction, it completely failed to explain black-body radiation (how hot objects emit specific colors of light) and the photoelectric effect.

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Worked Example: Energy of a Mole of Photons

Calculate energy using E=hv and Avogadro's number.

Problem. Calculate the energy of one mole of photons of radiation whose frequency is $5 \times 10^{14} \text{ Hz}$ .

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← previousDiscovery Of Particles & Early Models next →The Photoelectric Effect

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Worked Example: Broadcasting Frequencies

Calculate wavelength from frequency.

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reading

Faded Example: Wavenumber and Frequency

Calculate wavenumber and frequency from wavelength in Angstroms.

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content

Worked Example: Energy of a Mole of Photons

Calculate energy using E=hv and Avogadro's number.

Problem. Calculate the energy of one mole of photons of radiation whose frequency is $5 \times 10^{14} \text{ Hz}$ .

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