Frequently Asked Questions on Heisenberg’s Uncertainty Principle

This principle has a great significance in modern physics, especially quantum physics. It helps us understand the physical world in a better manner, which is not possible by using only classical physics. Heisenberg’s Uncertainty principle implies that the more precisely we determine the position of any particle, the less precisely we can determine its position. However, this exceptional rule is only applicable for microscopic particles and not for macroscopic particles. The principle is based on the wave-particle duality of matter that states the dual nature of matter i.e., wave and particles. In this article, we shall study the frequently asked questions on Heisenberg’s Uncertainty principle and its examples.

Frequently Asked Questions on Heisenberg’s Uncertainty Principle

Question: What Is Heisenberg’s Uncertainty Principle?

Answer: Heisenberg’s Uncertainty principle, as published by Werner Heisenberg in 1927, states that it is impossible to determine both the position and momentum of any particle simultaneously. Heisenberg’s principle is also applicable for the relation of energy and time. The equation of Heisenberg’s uncertainty principle is as follows:

Δ p. Δ x ≥ h/4π.

Δ t ΔE ≥ h/4π

Where h= Planck’s constant

Δ= Uncertainty.

Question: The given uncertainty of a proton is 4 × 103 m/s. Calculate the minimum uncertainty involved in the calculation of the position of the proton?

Answer: According to the question,

  Δvx= 4× 103 m/s.

=6.63× 10-34J/s.

We know that mass of the proton= 1.67262 × 10−27 kg

From the principle of uncertainty,

Δx × Δvx = h/4πm

Δx = h/4πm Δvx

Δx = 7.9× 10-12 m/s.

Answer: The minimum uncertainty involved in the calculation of the position of the proton is  7.9× 10-12 m.

Question: According to the Heisenberg uncertainty principle, it is impossible to calculate the position and velocity of an electron at the same time. Give reason.

Answer: According to Bohr’s model, the electron is a material particle and the calculation of its momentum and position at the same time is possible. However, de-Broglie declared the wave nature of the electron and concluded that it is impossible to simultaneously calculate the exact position and velocity of the electron. In 1927, Heisenberg gave his principle that states that the determination of both position and momentum of particles at the same time is impossible. This is simply because the electrons do not possess any definite position and direction of motion at the same time.

Question: Define the momentum of an object.

Answer: 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 i.e., 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.

Question: Define the conservation of linear momentum.

Answer: Conservation of Linear Momentum is like the conservation of energy which states that in an isolated system, the total momentum of the system remains unchanged. The total momentum of any system is the sum of the individual momenta of several objects in that system. The Conservation of Linear Momentum applies to different interactions such as collisions and separations due to explosive forces. The conservation of linear momentum has several applications such as in the launching of rockets and a collision and coalescence of two particles with known momentum. This law can help determine the momentum of the coalesced body.

Question: A given proton has an uncertainty of 20 pm. Determine the uncertainty in the speed of protons 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

Δp ≥ 2.6364×10-24 (kg⋅ m/s)

mΔv ≥ 2.6364×10-24 (kg⋅ m/s)

Or, 

Δv ≥ 2893962.67837 m/s

Δv ≈ 2.9×106 m/s

The uncertainty in the speed of protons using Heisenberg’s uncertainty principle is 2.9×106 m/s.

Question: Why is Heisenberg’s uncertainty principle only applicable for smaller or microscopic molecules and not for macroscopic molecules?

Answer: The Heisenberg uncertainty principle is only applicable for smaller or microscopic molecules and not for macroscopic molecules because the Planck’s constant in it is only for very small particles. In such a way, uncertainties in the position and momentum of small objects are difficult to determine experimentally.

Conclusion

Heisenberg’s uncertainty principle states that it is impossible to determine the position and momentum of any particle at the same time with absolute accuracy. The principle was stated by the German physicist and philosopher, Werner Heisenberg in 1927, and is of great significance in quantum physics. The principle is based on the wave-particle duality i.e., stating the dual nature of matter (waves and particles). Study the article to know about some of the Frequently Asked Questions on Heisenberg’s Uncertainty Principle.