What is Heisenberg’s Uncertainty Principle

Heisenberg’s principle of uncertainty, introduced in 1927, simply states that the more precisely we determine the position of any particle, the less precise we can determine its momentum from the given initial conditions. The Heisenberg uncertainty principle inherits from the theories of wave-like systems that state the matter wave nature of all the quantum objects. Thus, we can say that Heisenberg’s uncertainty principle has its deep root in the field of quantum mechanics of physics.

Heisenberg’s principle discusses the fundamental properties of quantum systems instead of some observational success of the technology. We cannot easily apply this rule in our daily lives, but it has a great significance for small particles such as atoms and subatomic particles. Heisenberg’s principle is contrary to classical Newton physics. According to classical Newton physics, all the particles are measurable to an arbitrary uncertainty in the presence of the best equipment. The laws of quantum physics and classical physics have a great contrast; however, the study of quantum physics greatly helped us better understand the physical world. Let’s study the Heisenberg uncertainty principle importance in brief.

What Is Heisenberg’s uncertainty principle?

The Heisenberg uncertainty principle was published in 1927, stating that it is impossible to assign simultaneous values to both position and momentum in a physical system. These quantities will definitely contain some small uncertainties. This relationship is also applicable to the relation between energy and time. This means that it is impossible to determine the precise energy of any system in a definite amount of time. Heisenberg defined these uncertainties as having value correspondence to Planck’s constant divided by 4π.

Δ p. Δ x ≥ h/4π.

Where h= Planck’s constant

Δp = Uncertainty in momentum.

Δx = Uncertainty in position.

The momentum of an object: Linear momentum is the value obtained by the product of any system’s mass with its velocity. Thus, it is clear that it is directly proportional to both mass and velocity. It is a vector quantity (a quantity that has both magnitude and direction). The symbol used for denoting the linear momentum is ‘p’, and its unit is kilogram metre per second (kg. m/s), i.e. the combined units of mass and velocity. However, in a closed system, which is a system in which there is no exchange or transfer of matter, momentum remains unchanged.

p=mv

where p= Linear momentum,

m= mass of the particle and

v= velocity of the particle.

Planck’s constant: The Planck’s constant is an important physical constant in quantum physics, denoted by h. This constant describes the behaviour of particles and waves on the atomic level. This Planck’s constant is the product of energy by time and is therefore called the elementary quantum of action. Its unit is a metre-kilogram-second, and the exact value is 6.62607015 × 10−34 joule second.

Wave-like particle duality: The uncertainty principle arises from the wave-like particle duality that states that every particle will have an associated wave. These particles are mostly present in the places with the highest undulations of the wave. Moreover, the more ill-defined wavelength will have more intense undulations of the wave. This helps in the determination of the momentum of any particle.

Heisenberg’s uncertainty principle importance

• It rules out the definite paths of electrons and other subatomic particles

• It helps in the determination of the probability of the position of any particle at a particular time. For example, if we know the position of any particle and its velocity at the time, then we can determine the position of that particle after some time

• Heisenberg’s principle has its importance only for microscopic particles and not for macroscopic particles

Solved questions on Heisenberg’s uncertainty principle

Question 1: A given neutron has an uncertainty of 20 pm. Determine the uncertainty in the speed of the neutron using Heisenberg’s uncertainty principle.

Solution:

Mathematically, the Heisenberg uncertainty principle is:

Δ x. Δ p ≥ h/4π

According to the question,

Δ x =20 pm

Applying Heisenberg’s Uncertainty principle,

Δ x. Δ p ≥ h/4π

Δ p≥ h/ 4πΔ x

Δ p≥

Δp≥2.6364×10−24 (kg⋅ m/s)

mΔv≥2.6364×10−24 (kg⋅ m/s)

Or, 

Δv≥2893962.67837m/s

Δv≈2.9×106 m/s

Answer: The uncertainty in the speed of the neutron using Heisenberg’s uncertainty principle shall be Δv≈2.9×106 m/s.

Question 2: The uncertainty in the momentum (say Δp) of a 0.5 kg tennis ball travelling at 20 m/s is 1×10−6 of its momentum. Determine the Δx or the uncertainty in position?

Solution:

According to the Question:

v = 20 m/s,

m = 0.5 kg,

h = 6.62607004 × 10-34 m2 kg / s (Planck’s constant)

Δp =p×1×10−6

P = m×v

= 0.5×20

= 10kg m/s

Δp = 10 × 1 × 10−6

Δp = 10-5

Formula of Heisenberg uncertainty principle,

Δ x. Δ p ≥ h/4π

Δ x≥ h/4π Δ p

Δ x≥0.527×10-29m

Answer: The uncertainty in the position of a 0.5 kg tennis ball travelling at 20 m/s is 0.527×10-29 m

Conclusion

According to Heisenberg’s uncertainty principle, it is impossible to determine the position and momentum of any particle at the same time. In other words, we can say that the more precisely we determine the momentum, the less precise the position of that particle. The principle derived from the wave-like nature of particles has a great significance in quantum mechanics. Quantum mechanics greatly differs from classical physics and helps in a better understanding of the physical world. Heisenberg’s uncertainty principle importance is only for microscopic particles, not macroscopic particles.