All About Heisenberg Uncertainty Principle : Defination, Formula , And Derivation

According to Heisenberg’s uncertainty principle, it is impossible to precisely measure or calculate an object’s position and momentum. The wave – particle duality of matter underpins this principle. Although Heisenberg’s uncertainty principle could be ignored in macroscopic world (uncertainties in the velocity and position of objects with significantly larger masses are minimal), it is extremely important in the quantum world. Because atoms and subatomic particles have such little masses, any improvement in location accuracy will be matched by a rise in uncertainty related with their velocities.

Heisenberg Uncertainty Principle

Heisenberg’s uncertainty principle is also known as the indeterminacy principle or uncertainty principle. In 1927, Werner Heisenberg, a German scientist, proposed his hypothesis. He claimed that the object’s position and velocity could not be reliably determined at the same time, according to his theory. According to him, this is also true at the subatomic level, where we can’t estimate both the position and velocity of subatomic particles like electrons, protons, and neutrons at the same time. At a specific time, we can either find the actual speed or the position.

Definition

We can’t know the position & momentum of a small particle at the same time, according to Heisenberg’s Uncertainty Principle. 

It means that we won’t be able to calculate the momentum if we can’t locate the particle’s position, and we won’t be capable of measuring the momentum if we can’t find the position. Both of them are impossible to quantify with arbitrary precision.

Formula

The Heisenberg uncertainty principle formula is given as;

∆x×∆p≥h4π

As we know, momentum p=mv

Therefore,

∆x×∆mv≥h4π

∆x = uncertainty in the position

∆p = uncertainty in momentum

m = mass

v = velocity

Momentum of an Object

An object’s momentum is defined as the product of its mass (described by m = F/a) and its velocity. It has a magnitude & a direction, just like velocity. In practice, momentum can be defined as an object’s proclivity to continue on its current course through space. The more the force necessary to change an object’s velocity, the greater the force needed to change its velocity.

Momentum formula 

The momentum formula is given as

p = mv 

Here, 

= momentum

= mass of body

= velocity of body

Change in momentum is given as

∆p=pf–pi=m(vf – vi) = m∆v

Atoms and Subatomic Particles

Atoms

The word atom comes from the Greek word atomos, that literally means “indivisible.” Atoms are the basic unit of matter which can be separated while still retaining the bulk’s chemical properties. Atoms are the tiniest units of matter that may be separated without releasing electrically charged particles. Negatively charged electrons, positively charged protons and, neutral neutrons are the three types of particles that make up an atom. Atoms can unite to produce molecules with chemical properties that are unique from the composite elements.

Subatomic Particles

A subatomic particle is a particle with a size smaller than that of an atom. Protons, neutrons and electrons are the three subatomic particles that typically make up an atom.

Proton

The nucleus of an atom is made up of protons and neutrons, which are also known as nucleons. When Ernest Rutherford was conducting his gold foil experiment in 1919, he discovered proton for the first time. Positive alpha particles were deflected when he projected alpha particles (named helium nuclei) towards gold foil.

Electron

In the year 1897, John Thomson discovered the electron. They are negatively charged subatomic particles that rotate around an atom’s nucleus and are found in the electron cloud, which is the region surrounding the nucleus. An atom can lose or gain electrons, resulting in the formation of an ion. These positively and negatively charged ions join forces to form chemical bonds.

Neutron

James Chadwick discovered the neutron in 1932, and it is found in the nucleus alongside the protons. The nucleons are made up of neutrons and protons. They have no charge like a proton or an electron. The neutron determines an atom’s isotope and stability. In an atom, the number of neutrons does not always equal the number of protons.

Conclusion

Heisenberg’s uncertainty principle is named after him. In 1927, Werner Heisenberg, a German scientist, articulated this idea. This principle states that we can concurrently determine multiple things about particles, and it is one of the most well-known conclusions of quantum mechanics. The process of measuring a different provided variable of particles, according to this theory, contains inherent uncertainty.

Momentum of an object is given as

p = mv 

The Heisenberg uncertainty principle formula is given as;

∆x×∆p≥h4π

A subatomic particle is a particle whose size is smaller as compared to that of an atom.