Wave Particle Duality of Light

Wave-Particle Duality of Light: Particle properties of light

Light mostly acts as a wave, but it may also be thought of as a collection of small energy packets known as photons. Photons have no mass but convey a set quantity of energy.

The amount of energy carried by a photon is directly proportional to the photon's frequency and inversely proportional to its wavelength. To calculate a photon's energy, we use the following equations:

\[E = hf\]

where:

• It is the photon's energy [joules].
• h is the Planck constant: \(6.62607015 \cdot 10^{-34} [m ^ 2 \cdot kg \cdot s ^ {-1}]\).
• f is the frequency [Hertz].

\[E = \frac{hc}{\lambda}\]

where:

• E is the photon's energy (Joules).
• λ is the photon's wavelength (meters).
• c is the speed of light in a vacuum (299,792,458 meters per second).
• h is the Planck constant : \(6.62607015 \cdot 10^{-34} [m ^ 2 \cdot kg \cdot s ^ {-1}]\).

Wave-Particle Duality of Light: Wave properties of light

The four classical light properties as a wave are reflection, refraction, diffraction, and interference.

• Reflection: this is one of the properties of light you can see every day. It occurs when light hits a surface and comes back from that surface. This 'coming back' is the reflection, which happens at various angles.

  If the surface is flat and bright, as in the case of water, glass, or polished metal, the light will be reflected at the same angle at which it hit the surface. This is known as specular reflection.

  Diffuse reflection, on the other hand, is when light strikes a surface that is not as flat and bright and reflects in many different directions.

• Refraction: This is another property of light that you come across almost every day. You can observe this when, looking into a mirror, you see an object displaced from its original position. For light refraction, the light follows Snell's law. According to Snell's law, if θ is the angle from the boundary normal, v is the velocity of light in the respective medium (meter / second), and n is the refractive index of the respective medium (which is unitless), the relation between them is as shown below.

• Diffraction and Interference: waves, be they water, sound, light, or other waves, do not always create sharp shadows. In fact, waves occurring on one side of a tiny aperture radiate away in all sorts of ways on the other side. This is referred to as diffraction.

  Interference occurs when light meets an obstacle that contains two tiny slits separated by a distance d . The wavelets emanating towards each other interfere either constructively or destructively.

  If you put a screen behind the two tiny slits, there will be dark and bright stripes, with the dark stripes being caused by constructive interference and the bright stripes by destructive interference.

History of Wave-Particle Duality

Current scientific thinking, as advanced by Max Planck, Albert Einstein, Louis de Broglie, Arthur Compton, Niels Bohr, Erwin Schrödinger, and others, holds that all particles have both a wave and a particle nature. This behavior has been observed not just in elementary particles but also in complex ones, such as atoms and molecules.

Wave-Particle Duality of Light: Planck's law and black body radiation

In 1900, Max Planck formulated what is known as Planck's radiation law to explain the spectral-energy distribution of a blackbody's radiation. A blackbody is a hypothetical substance, which absorbs all radiant energy that strikes it, cools to an equilibrium temperature, and re-emits the energy as rapidly as it receives it.

Given Planck's constant (h = 6.62607015 * 10 ^ -34), the speed of light (c = 299792458 m / s), the Boltzmann constant (k = 1.38064852 * 10 ^ -23m ^ 2kgs ^ -2K ^ -1), and the absolute temperature (T), Planck's law for energy Eλ emitted per unit volume by a cavity of a blackbody in the wavelength interval from to λ + Δλ may be expressed as follows:

\[E_{\lambda} = \frac{8 \pi hc}{\lambda^5} \cdot \frac{1}{exp(hc/kT \lambda) - 1}\]

Most of the radiation emitted by a blackbody at temperatures up to several hundred degrees is in the infrared region of the electromagnetic spectrum. At increasing temperatures, the total radiated energy rises, and the intensity peak of the emitted spectrum changes to shorter wavelengths, resulting in visible light being released in greater amounts.

Wave-Particle Duality of Light: Photoelectric effect

While Planck used atoms and a quantized electromagnetic field to solve the ultraviolet crisis, most modern physicists concluded that Planck's model of 'light quanta' had inconsistencies. In 1905, Albert Einstein took Plank's blackbody model and used it to develop his solution for another massive problem: the photoelectric effect. This says that when atoms absorb energy from light, electrons are emitted from atoms.

Einstein's explanation of the photoelectric effect: Einstein provided an explanation for the photoelectric effect by postulating the existence of photons, quanta of light energy with particulate qualities. He also stated that electrons could receive energy from an electromagnetic field only in discrete units (quanta or photons). This led to the equation below:

\[E = hf\]

where E is the amount of energy, f is the frequency of light (Hertz), and his Planck's constant (\(6.626 \cdot 10 ^{ -34}\)).

Wave-Particle Duality of Light: De Broglie's hypothesis

In 1924, Louis-Victor de Broglie came up with de Broglie's hypothesis, which made a big contribution to quantum physics and said that small particles, such as electrons, can display wave properties. He generalized Einstein's equation of energy and formalized it to obtain the wavelength of a particle:

\[\lambda = \frac{h}{mv}\]

where λ is the particle's wavelength, h is Planck's constant (\(6.62607004 \cdot 10 ^ {-34} m ^ 2 kg / s\)), and m is the mass of the particle moving at a velocity v.

Wave-Particle Duality of Light: Heisenberg's uncertainty principle

In 1927, Werner Heisenberg came up with the uncertainty principle, a central idea in quantum mechanics. According to the principle, you can't know the exact position and the momentum of a particle at the same time. His equation, where Δ indicates standard deviation, x and p are a particle's position and linear momentum respectively, and his Planck's constant (\(6.62607004 \cdot 10 ^ {-34} m ^ 2 kg / s\)), is shown below.

\[\Delta x \Delta p \geq \frac{h}{4 \pi}\]