# Planck's Quantum Theory

## Max Planck showed that the energy of light is proportional to its frequency, also showing that light exists in discrete quanta of energy.

#### Key Points

• In the late 18th century, many physicists believed that they had made great progress in physics, and there wasn't much more to be discovered. However, by the early 20th century, physicists discovered that the laws of classical mechanics break down in the atomic world.

• The photoelectric effect could not be rationalized based on the theories of light that were prevalent when it was discovered, as an increase in the intensity of light did not lead to the same outcome as an increase in the energy of the light.

• Planck postulated that the energy of light is proportional to the frequency, and the constant that relates them is known as Planck's constant, h. His work led to Albert Einstein determining that light exists in discrete quanta of energy, or photons.

#### Terms

• The emission of electrons from the surface of a material following the absorption of electromagnetic radiation

• Radiation (quantized as photons) consisting of oscillating electric and magnetic fields oriented perpendicularly to each other, moving through space.

#### Figures

1. ##### Wavelength of a wave

The distance used to determine the wavelength of a wave is shown. Light has many properties associated with its wave nature, and the wavelength in part determines these properties.

2. ##### Emission spectrum of nitrogen gas

Each wavelength of light emitted (each colored line) corresponds to a transition of an electron from one energy level to another, releasing a quantum of light with defined energy (color).

In the late 18th century, many physicists believed that they had made great progress in physics, and there wasn't much more that needed to be discovered. The classical physics at the time was widely accepted in the scientific community. However, by the early 20th century, physicists discovered that the laws of classical mechanics break down in the atomic world, and experiments such as the photoelectric effect completely contradict the laws of classical physics. As a result of these crises, physicists began to construct new laws of physics which would apply to the atomic world; these theories would be collectively known as quantum mechanics. Quantum mechanics, in some ways, completely changed the way physicists viewed the universe, and it also marked the end of the idea of a clockwork universe (the idea that universe was predictable).

Electromagnetic radiation (ER) is a form of energy that sometimes acts like a wave, and other times acts like a particle. Visible light is a well-known example. All forms of ER have two inversely proportional properties: wavelength and frequency. Wavelength is the distance from one wave peak to the next, which can be measured in meters. Frequency is the number of waves that pass by a given point each second.Figure 1 Since wavelength and frequency are inversely related, their product (multiplication) always equals a constant—specifically, 3.0 x 108 m/sec, which is better known as the speed of light. The wavelength and frequency of any specific occurrence of ER determine its position on the electromagnetic spectrum. Again, the conversion of the wavelength of a light is determined by using, $c=λv$

where c is the constant 3.0 x 108 m/sec, the speed of light in a vacuum, λ = wavelength in meters and v=frequency in hertz, 1/s.  It is important to note that using this equation, one can determine the wavelength of light in frequency.

## The Discovery of the Quantum

So far we have only discussed the wave characteristics of energy. However, the wave model cannot account for something known as the photoelectric effect. This effect is observed when light focused on certain metals apparently causes electrons to be emitted. (For a more comprehensive discussion of the photoelectric effect, see the associated atom in this module.) For each metal, there is a minimum threshold frequency of electromagnetic radiation that is needed to be shone on it in order for it to emit electrons. One could not replace a certain amount of light at one frequency with twice as much light of half the frequency. If light only acts as a wave, the effect of light should be cumulative—the light should add up, little by little, until it causes electrons to be emitted. Instead, there is a clear-cut minimum of the frequency of light that triggers the electron emissions. The implication of this is that frequency is directly linked to energy, with the higher light frequencies having more energy. This observation led to the discovery of the minimum amount of energy that could be gained or lost by an atom. Max Planck named this minimum amount the "quantum," plural "quanta," meaning "how much." One photon of light carries exactly one quantum of energy.

Planck is considered the father of the Quantum Theory. According to Planck, each energy element E is proportional to its frequency ν: E=hv, where h is Planck's constant. Planck (cautiously) insisted that this was simply an aspect of the processes of absorption and emission of radiation, and had nothing to do with the physical reality of the radiation itself. However, in 1905 Albert Einstein interpreted Planck's quantum hypothesis realistically and used it to explain the photoelectric effect, in which shining light on certain materials can eject electrons from the material.

## More Evidence for a Particle Theory of Energy

When an electric current is passed through a gas, some of the gas molecules' electrons move from their ground state to an excited state that is further away from their nuclei. When the electrons return to the ground state, they emit energy of various wavelengths. A prism can be used to separate the wavelengths, making them easy to identify. If light acted only as a wave, then there should have been a continuous rainbow created by the prism. Instead, there were discrete lines created by different wavelengths. This is because electrons release specific wavelengths of light when moving from an excited state to a ground state.Figure 2

#### Key Term Glossary

atom
the smallest possible amount of matter that still retains its identity as a chemical element, now known to consist of a nucleus surrounded by electrons
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constant
Consistently recurring over time; persistent
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electromagnetic
Pertaining to electromagnetism.
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Radiation (quantized as photons) consisting of oscillating electric and magnetic fields oriented perpendicularly to each other, moving through space.
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electron
The subatomic particle having a negative charge and orbiting the nucleus; the flow of electrons in a conductor constitutes electricity.
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element
Any one of the simplest chemical substances that cannot be decomposed in a chemical reaction or by any chemical means, and are made up of atoms all having the same number of protons.
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emission
That which is emitted or sent out.
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energy
a quantity that denotes the ability to do work and is measured in a unit dimensioned in mass × distance²/time² (ML²/T²) or the equivalent
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excited state
any state of a particle or system of particles that has a higher energy than that of its ground state.
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frequency
The number of occurrences of a repeating event per unit of time.
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gas
Matter in a state intermediate between liquid and plasma that can be contained only if it is fully surrounded by a solid (or held together by gravitational pull); it can condense into a liquid, or can (rarely) become a solid directly.
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ground state
the stationary state of lowest energy of a particle or system of particles.
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metal
Any of a number of chemical elements in the periodic table that form a metallic bond with other metal atoms; generally shiny, somewhat malleable and hard, often a conductor of heat and electricity
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molecule
the smallest particle of a specific element or compound that retains the chemical properties of that element or compound; two or more atoms held together by chemical bonds
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photoelectric effect
The emission of electrons from the surface of a material following the absorption of electromagnetic radiation
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photon
The quantum of light and other electromagnetic energy, regarded as a discrete particle having zero rest mass, no electric charge, and an indefinitely long lifetime. It is a gauge boson.
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product
a chemical substance formed as a result of a chemical reaction
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quanta
discrete packets with energy stored inside
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quantum
the smallest possible, and therefore indivisible, unit of a given quantity or quantifiable phenomenon
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quantum theory
A theory developed in early 20th century, according to which nuclear and radiation phenomena can be explained by assuming that energy only occurs in discrete amounts called quanta.
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spectrum
Specifically, a range of colours representing light (electromagnetic radiation) of contiguous frequencies; hence electromagnetic spectrum, visible spectrum, ultraviolet spectrum, etc.
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state
The physical property of matter as solid, liquid, gas or plasma
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wave
A shape that alternatingly curves in opposite directions.
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wavelength
the distance between one peak or trough of a travelling oscillation and the next; it is often designated in physics as λ, and corresponds to the velocity divided by the frequency