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# Wave Particle Duality of Light

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Wave-particle duality is one of the most important ideas in quantum theory. It states that, just as light has the properties of wave and particle, so matter also has those two properties, which have been observed not only in elementary particles but also in complex ones, such as atoms and molecules.

## What is the wave-particle duality of light?

The concept of the wave-particle duality of light says that light possesses both wave and particle properties, even though we cannot observe both at the same time.

### 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 : 6.6260701510-34 [m ^ 2 * kg * 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 * 10 ^ -34 (m ^ 2kgs ^ -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.

A real-life example of reflection. flickr.com

• 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.

A real-life example of refraction. flickr.com

• 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.

Two-slit interference pattern. -StudySmarter Originals

## 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:

${E}_{\lambda }=\frac{8\pi hc}{{\lambda }^{5}}·\frac{1}{exp\left(hc/kT\lambda \right)-1}$

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 * 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 * 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 * 10 ^ -34 m ^ 2 kg / s), is shown below.

$∆x∆p\ge \frac{h}{4\pi }$

## Wave-Particle Duality - Key takeaways

• Wave-particle duality states that light and matter have both wave and particle properties, even though you cannot observe them at the same time.
• Although light is most commonly thought of as a wave, it may also be conceived of as a collection of tiny energy packets known as photons.
• Amplitude, wavelength, and frequency are the three measurable properties of wave motion. Reflection, refraction, diffraction, and interference are the additional wave properties of light.
• The photoelectric effect is the effect that describes the emission of electrons from a metal's surface when it is impacted by the light of a certain frequency. Photoelectrons are the name given to the emitted electrons.
• According to the uncertainty principle, even in theory, the position and velocity of an item cannot be measured accurately at the same time.

Light can be understood both as a wave and a particle.

Louis de Broglie suggested that electrons and other discrete pieces of matter, which had formerly only been thought of as material particles, had wave characteristics, such as wavelength and frequency.

Light and matter have properties that are both wavelike and particle-like.

## Final Wave Particle Duality of Light Quiz

Question

When was wave-particle duality discovered?

In 1924.

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Question

Can you observe both wave and particle properties of light at the same time?

No, you can't.

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Question

What is a light particle called?

A photon.

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Question

Is it true that photons have no mass but convey a set quantity of energy?

Yes, it is.

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Question

The amount of energy carried by a photon is directly proportional to what?

It is directly proportional to the photon's electromagnetic frequency while also being inversely proportional to its wavelength.

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Question

Which is the symbol for Planck's constant?

(h).

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Question

What is Planck's constant equal to?

It is equal to 6.62607015 * 10^-34 (m^2 kg s^-1).

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Question

Light refraction follows which law?

Snell's law.

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Question

What are the symbols for energy and frequency?

E and f.

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Question

What is the speed of light in a vacuum?

It is 3.00 * 10^8 ms^-1.

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Question

What is the symbol for the speed of light?

c

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Question

Is it true that light moves slower than c in any substance other than a vacuum?

Yes, it is.

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What are the two types of reflection?

Specular reflection and diffuse reflection.

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Question

What is it called when the light reflects at the same angle that it came into contact with the surface?

Specular reflection.

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Question

What is it called when the light hits a rough surface and reflects in many different directions?

Diffuse reflection.

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Question

What is it called when you look through a mirror and see an object displaced from its original position?

Refraction.

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Question

When was the photoelectric effect discovered?

In 1905.

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Question

Which principle states that you can't know the exact position and the momentum of a particle at the same time?

Heisenberg's uncertainty principle.

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Question

When was Heisenberg's uncertainty principle proposed?

In 1927.

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Question

What is the name of a hypothetical substance that absorbs all radiant energy that strikes it?

Blackbody.

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Question

A photoelectron with a kinetic energy of 5.0eV is emitted from a gold plate. Determine the energy in joules for the photon that impacted the plate.

1.616 * 10 ^ -18 [J].

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Question

A photoelectron with a kinetic energy of 5.0eV is emitted from a copper plate. Determine the frequency in Hertz for the light that impacted the plate.

2.34 * 10 ^ 15 Hertz.

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Which of the following scientists first observed the photoelectric effect?

Heinrich Hertz.

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Which of the following scientists proved the photoelectric effect with his experiment?

Robert Millikan.

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Question

Which of the following concepts cannot be explained by the wave theory of light?

Threshold frequency.

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Question

Which scientist explained the photoelectric effect?

Albert Einstein.

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Question

What is the symbol for the Planck constant?

h.

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Question

What is the symbol for frequency?

f.

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What is the name for the specific value of energy that is required to release a photoelectron from the metal plate?

Work function.

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What is the name for the frequency that provides the work function energy?

Threshold frequency.

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Question

What is the name for the basic unit of light?

Photon.

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Question

Which of the following is not one of the applications of the photoelectric effect?

PC monitors.

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Question

What is the relationship between the kinetic energy of a photoelectron and the frequency of the light?

The kinetic energy is directly proportional to the frequency of the light.

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Question

Robert Millikan, seeking to disprove the photoelectric effect, conducted his experiment in which conditions?

In a vacuum.

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Question

Which equation is used to calculate the kinetic energy of a photoelectron?

E = hf, where h is the Planck constant and f the frequency of the light.

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Question

Which of the following describes the wavelength of an electron's wavelength ratio to the wavelength of light?

It is 100,000 times smaller.

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Question

Which of the following is not one of the advantages of using electron microscopes?

They can create coloured images.

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Question

Which of the following is not one of the disadvantages of using electron microscopes?

They can't produce high-resolution images.

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Question

What is the purpose of the first lens in transmission electron microscopes?

To convert electrons into a more powerful beam.

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What is the purpose of the lower coil in scanning electron microscopes?

To steer the electron beam from side to side.

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Who invented the first prototype of electron microscopes?

Ernst Ruska.

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When was the first electron microscope invented?

1931.

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Question

What are the two types of electron microscope?

The transmission electron microscope and the scanning electron microscope.

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Can electron microscopes provide images in colour?

No they can't.

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Question

Can electron microscopes be used to analyse living specimens?

No.

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Question

Why can't electron microscopes analyse live specimens?

Because electron microscopes have to analyze in a vacuum.

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Question

The resolution we can get using electron microscopes is in the range of up to which of the following (fill in the blank)?

2.2 [nm]

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Can electron microscopes create electron micrographs?

Yes.

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Question

In transmission electron microscopes, what does the cathode consist of in order to create a beam of electrons?

Heated filament.

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Can images created with electron microscopes be viewed through a monitor?

Yes.

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