Wave-Particle Duality

Physics: IB Diploma Higher Level, topic 5.3.4

Wave-Particle Duality - Light

Interference and diffraction show that light is a wave. The photoelectric effect shows that light must be a particle. Quantum physics means light can be both a wave and a particle at the same time.

Light as a wave

Experiments such as shining light through a diffraction grating show us that light must be a wave.
Light must diffract through the grating and then interfere constructively and destructively to produce bands of light and dark.
Only a wave would be able to do this.
A classical particle (e.g. a tennis ball) cannot interfere with another tennis ball to produce one larger one!

Light as a particle

The photoelectric effect displays that light must be a particle.
The experiment shows that light particles (photons) have a one-on-one interaction with an electron on the metal surface.

Particle Duality

In 1924, physicist Louis de Broglie suggested that particles might exhibit wave properties, such as diffraction. At the time, scientists dismissed his theory. But electron diffraction and other experiments showed de Broglie was right.

De Broglie wavelength

De Broglie suggested that any particle with a momentum, mv, must have an associated wavelength, λ, given by:
$\lambda = \frac{h}{mv}$

$Electron diffraction experiments$

Electron diffraction experiments

After de Broglie came up with this theory, other scientists set up experiments trying to prove (or disprove) his equation.
These experiments showed that electrons did diffract like waves through a grating, and had a wavelength equal to what de Broglie had suggested.
Given this experimental evidence, scientists changed their minds and accepted de Broglie's theory.

Electron Orbitals

Electrons can exist only in locations where they interfere constructively.

Electron orbits

How does this affect electrons in atomic orbits?
When an electron is bound to an atom, its wavelength must fit into a small space like a standing wave on a string. - Allowed orbits are those orbits in which an electron constructively interferes with itself.
Not all orbits produce constructive interference.
Only certain orbits are allowed, meaning the orbits are quantized.

Quantization

For a circular orbit, the electron waves must fit an integer number of times into the circumference of the orbit:
$n\lambda_n = 2\pi r_n$
Where λ_n is the electron’s wavelength and r_n is the radius of that circular orbit.

Quantization 2

Substituting for the de Broglie wavelength of an electron we have:
$n\frac{h}{m_e \nu}=2\pi r_n$
Substituting for the angular momentum L we can write:
$L = m_e\nu r_n =n\frac{h}{2\pi} \;(n=1,2,3...)$
So the angular momentum for electrons in orbit must be quantized.

Test yourself on Wave-Particle Duality

Which of these statements are true about light?
Which of the following is true of particle duality?
What kind of waves are formed by electrons in orbit?
Which of the following is the correct equation for the angular momentum of an electron in orbit?

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