Physics of the Smallest: Basics of Quantum Physics

The special theory of relativity, introduced in 1905 by Albert Einstein, revolutionalized our ideas about space and time. It tells us that for a moving object time slows down. It also tells us that the mass of an object moving with some velocity is greater than its rest mass (at velocity equals zero) and size is also smaller than its size at rest.

It was introduced due to the failure of classical Physics at very high speeds (near to that of the speed of light), in other words, classical physics can only be applied to daily life situations.

But, Special relativity is not only applicable to the objects moving with very high velocity, but we can also apply the equations on daily life situations. But, in this case, the results are (almost) similar to that of classical Physics. In other words, the equations of Relativity, when applied on daily life situations, reduce to the equations of classical Physics.

But, we still use classical physics due to its simplicity because the equations of classical Physics are very simpler than the equations of relativity.

Classical Physics isn’t applicable to very high-speed situations. But, there is another problem with classical Physics, it is anot applicable to the ‘small scale of the universe’ also . It isn’t applicable to atoms and objects and particles smaller than atoms. To be more technical and exact, classical Physics isn’t applicable on objects with size 10-9 metres and smaller than this. This problem is not only with classical Physics but also with the general theory of relativity. (But, the special theory of relativity works fine on the small-scale.)

The problem is with the general theory of relativity. General relativity isn’t consistent with particles of size 10-9 metres or smaller.

The ‘Physics of the smallest’ is ‘Quantum Physics’ or ‘Quantum Mechanics’, or simply QM. Actually, quantum Physics was first introduced in 1900. The idea of QM started five years before the idea of the theory of relativity. Einstein, himself had a very important role in QM. He also won the Nobel prize in Physics in 1921 for his work in QM in 1905 but he never won a Nobel prize for the greatest theory, GR (general relativity) or SR (special relativity).

The foundation of quantum Physics was laid by two German physicists, Max Planck and Albert Einstein.

This article mainly focuses on the basic concepts of Quantum Physics including, Planck’s Quantum Theory, Wave-Particle Duality and the Uncertainty Principle.


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The Need for Quantum Physics

To understand why QM was introduced, we should discuss a little bit about ‘Waves’.

A wave is a disturbance in a ‘Medium’ (like air or water) or ‘Field’ (like a gravitational field, electromagnetic field etc.).

So, how can a medium or field be disturbed? The answer is simple — when energy transfers from one place to another in that particular medium or field.

So, in other words, a wave is a transfer of energy from one place to another in a medium or field. A familiar example of a wave is a water wave which is produced when you drop anything in the water. A wave has ‘Crests’ (peaks) and ‘Troughs’ (bottom point).

A wave moves in ‘cycles’, that is, the medium or field (which is ‘disturbed’ by the wave) repeatedly moves up and down (for example water waves or light waves) or left and right (for example, sound waves).

The distance covered by a wave in one single cycle is called its ‘Wavelength’. Wavelength is also equal to the distance between two successive crests or troughs.

Another property of a wave is ‘Frequency’. Frequency is the number of cycles or ‘Oscillations’ completed by a wave in a single second.

One ‘Cycle’ or ‘Oscillation’ means moving to the extreme top (or right) position from the original position and then to the extreme bottom (or left) position and again back to the original position.

Time Period’ is the time taken by the wave to complete one cycle. It can be concluded now that frequency is just the inverse of the time period:

Frequency = 1  ∕ Time Period

And:

Time period = 1  ∕ Frequency

A wave is illustrated below.

According to the ‘Electromagnetic Wave Theory’ (developed by James Clerk Maxwell), light is also a wave. It disturbs the electromagnetic field. So, light is an electromagnetic wave or electromagnetic radiation.

According to this theory, light is emitted and absorbed ‘continuously’ (in the form of waves). It also states that the ‘Intensity’ (or brightness) of light is directly proportional to the energy of light, and, frequency and wavelength of light are independent of the energy.

Actually, light’s frequency and wavelength decide its colour. Every different colour has a different frequency (and wavelength).

The word ‘Electromagnetic Radiation’ is more correct than light because ‘Light’ generally refers to electromagnetic radiation of visible range, that is, the electromagnetic radiation that our eyes can observe. This frequency ranges from the colour red (Frequency = 43 × 1013 Hertz) to violet colour (Frequency = 75 × 1013 Hertz). The visible range of light contains seven colours — Red (Lowest Frequency), Yellow, Orange, Green, Blue, Indigo and Violet (Highest Frequency). The above list is in the order of increasing frequency (and decreasing wavelength).

The speed or velocity of a wave is equal to its frequency multiplied by its wavelength. Frequency of a wave is the velocity of the wave divided by its wavelength. The wavelength of a wave is the velocity of the wave divided by its frequency.

All the relations (above) can be written as:

  1. Velocity of a wave = Frequency of the wave × Wavelength of the wave
  2. Frequency of a wave = Velocity of the wave ∕ Wavelength of the wave
  3. Wavelength of a wave = Velocity of the wave ∕ Frequency of the wave

But, the electromagnetic wave theory, fails to explain some natural phenomena of light, namely, the ‘Black Body Radiation’ and the ‘Photoelectric Effect’.

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Black Body Radiation

A ‘Black Body’ is an object, which can perfectly absorb and radiates (emits) electromagnetic radiation (light) of any frequency. The electromagnetic radiation it emits is known as the ‘Black Body Radiation’.

When such an object, for example, an iron rod is heated, it firstly becomes red, on increasing the temperature, it becomes yellow and, on constantly increasing the temperature, the frequency of radiation increases and the rod finally starts to glow with blue light.

It should be noted that an increase in temperature means an increase in the (heat) energy.

According to electromagnetic wave theory, the frequency of radiation is independent of the energy. But, the frequency of radiation increases in the case of black body radiation with the increase in energy. So, electromagnetic wave theory is unable to explain the black body radiation.


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Photoelectric Effect

Photoelectric Effect’ is the emission of ‘electrons’ (a type of particle found in an atom) when light rays strike a metal surface. The emitted electrons are known as ‘Photoelectrons’. This effect was first discovered by Heinrich Hertz, a German Physicist.

In metals, a number of ‘free electrons’ are there, that is, the electrons which ‘feel’ very less attraction to the atom’s nucleus. As the free electrons are also (very weakly) bound to the nucleus, they require some minimum energy to leave the surface of metals because the ‘positively charged’ nucleus is continuously attracting the ‘negatively charged’ electrons.

But, it was observed that electrons are only ejected if the frequency of light is greater than particular ‘minimum frequency’, known as the ‘Threshold Frequency’ of a metal, that is, the ejection of electrons depends upon the frequency of light only. This means the emission of electrons has nothing to do with the intensity of light.

But, according to the electromagnetic wave theory, not frequency but intensity “decides”the energy of the light rays. So, electromagnetic wave theory is unable to explain this observation because according to this theory, only a minimum intensity should decide whether the electrons will be ejected or not.

Photoelectric effect is illustrated below.


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Planck’s Quantum Theory and the Dual Nature of Light

To explain the black body radiation, a German Physicist, Max Planck suggested that light is not emitted continuously in the form of waves, but, ‘discontinuously’ in some small ‘packets’ of energy known as ‘Quanta’ (singular of quanta is ‘quantum’). A ‘Quantum’ can be defined as the most fundamental unit of anything. One quantum of light is known as ‘Photon’. This means that light is made of particles known as photons.

Does this mean that light is not a wave? Actually, both things are correct. Light shows a ‘dual’ nature of both waves and particles. In other words, each photon is associated with a wave. There are many phenomena of light which can only be explained by wave theory (like Interference) and not by particle nature, and some can only be explained by particle nature.

Planck also suggested that the energy of a photon is directly proportional to the frequency of the corresponding light wave. That is, the greater the energy of the photon, the greater the frequency of the corresponding light wave, and vice versa. And, the relation between energy and frequency is given by:

Energy of a Photon = Planck’s Constant × Frequency of corresponding Light Wave

The above relation is also known as the ‘Einstein-Planck Relation’.

The numerical value (value without unit) of Planck’s constant is 6.6 × 10-34

If we put the value of frequency (in terms of  velocity and wavelength) in the above relation, we get:

Energy of a Photon = Planck’s Constant × (Velocity of the Light Wavelength of the corresponding light wave)

Now, as the energy is independent of intensity, the black body radiation can be explained as follows:

When a black body, like an iron rod, is heated, it starts to glow with red light first. As we increase the temperature, the energy increases, and hence, the frequency increases. So, the iron rod starts to glow with a light of higher frequency. The frequency of the radiation emitted will increase with temperature.

Using Planck’s Quantum Theory, Albert Einstein explained the photoelectric effect.

We know that free electrons require a minimum energy to leave the surface of the metal. And, as frequency and energy are directly proportional, light of a minimum frequency is required to eject electrons from the metal. As we strike light on the metal, the photons will strike the electrons and they will give their energy to the electrons and electrons will be ejected.


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Wave-Particle Duality

Max Planck and Albert Einstein laid the foundation for the development of Modern Physics.

But, the dual nature described in Planck’s Quantum theory was only about photons and electromagnetic waves.

In 1924, a French physicist, Louis de Broglie suggested that not only photons but the particles of matter (electrons, quarks and neutrinos, mainly) also exhibit dual nature of particle and wave. This hypothesis of de Broglie was a ‘generalization’ of Planck’s theory. So, the Einstein-Planck relation can be applied to any particle.

So, Einstein-Planck relation can be written as:

Energy of a matter particle = Planck’s Constant × Frequency of the corresponding matter wave 

When we will do some math on the Einstein-Planck relation and the Einstein Mass-Energy relation, we will get the following relation:

Wavelength of a matter wave = Planck’s Constant Momentum of the corresponding matter particle

The momentum of a particle is the mass of the particle multiplied by its velocity.

The above relation is also called ‘de Broglie’s Wavelength Relation’. The relation described is applicable to any type of  ‘fundamental particle’.

But, if matter shows dual nature, why can’t we observe the wave nature of matter in our daily life.

So, take an example of any bullet of four grams moving with a velocity of 400 metres per second. Consider its diameter is five centimetres. The mass of bullet in kilograms will be 0.004 kg.

So, its momentum will be 0.004 multiplied by 400, that is, 1.6 kg m/s (mass × velocity). Now, the wavelength of the corresponding wave will be only about 4 × 10-34 meters and the diameter of the bullet is five centimetres or 0.05 meters, which is much larger than its wavelength. So, here, absolutely, particle nature dominates.

So, for the objects far larger than an atom, particle nature dominates due to having large size and very short wavelength. The dual nature of particles and waves is called the ‘Wave-Particle Duality’.


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Heisenberg’s Uncertainty Principle

In 1814, a French mathematician Marquis de Laplace introduced the ‘Principle of Determinism’ in which he suggested that if we know the present state of the universe, then, using the correct laws of Physics, we can find the future or past state of the universe with 100 per cent certainty.

It seems to be true because, if we know the present position and momentum (that is, mass × velocity) of Earth, Sun and our Moon, we can find out when the next solar or lunar eclipse will take place by using Newton’s laws. Everyone was satisfied with this principle of determinism.

After developing his general theory of relativity and being awarded by the Nobel prize for the photoelectric effect in 1921, Einstein was doing research in quantum theory, but his research was interrupted by (another) German physicist, Werner Heisenberg in 1928 when Heisenberg presented his ‘Uncertainty Principle’.

It was the most important conclusion of Planck’s theory that was realized in 1928, by Heisenberg.

This principle states that we can’t measure the position and momentum of a particle with 100 per cent certainty. If we increase the certainty in one of these two, the certainty in the other quantity decreases.

There is a mathematical relation between uncertainty in position, momentum and Planck’s constant, which is:

Uncertainty in Position × Uncertainty in Momentum = always greater than Reduced Planck’s Constant ∕ 2

(Numerical value of the reduced Planck’s Constant is 1.0545718 × 10-34)

But, then why we can find out (with certainty) that when will next solar or lunar eclipse will take place using Newton’s laws?

Actually, there is uncertainty in the position and momentum of a particle because it also shows wave nature. If this is true, then obviously we can’t measure both the position and momentum of a particle precisely, because a wave is a transfer of energy in a medium or a field. So, when energy will be transferred, the medium or field will get ‘disturbed’. As a wave is nothing but a transfer of energy, so we can’t give a definite position to a wave. And because all particles also behave as waves, so, now particles don’t have any absolute location or position or momentum.

But, then why this doesn’t apply on objects far larger than atoms. This is because (as we discussed above) the size of large objects is much larger than the wavelength of their corresponding matter wave, so the uncertainty in their position and momentum is almost equal to zero.


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Author: Madhur Sorout

Madhur Sorout is an Eleventh Grader and the founder of the science website - Maddyz Physics (maddyzphysics.com). His main fascination lies in Physics mainly in the field of the general theory of relativity and topics related to it like Big Bang, Black Holes and Evolution of Universe. He likes to make out the meaning of what he sees in this universe. He loves to read books by Stephen Hawking, Neil deGrasse Tyson and other authors (and Physicists). A diehard fan of fiction, he also likes to play cricket also and he wants to continue down the route of research in Theoretical Astrophysics.

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