Select the correct statement(s) about Uncertainty principle....

Name: Problem 122, Chapter 3: Physical Chemistry for IIT JEE
Uploaded: 2022-01-30T06:11:36-08:00
Duration: 53 s
Channel: Hunza Gilgit
Description: Select the correct statement(s) about Uncertainty principle. a. The product of uncertainty in momentum in position is always constant b. This principle can explain why electron cannot exist in nucleus c. This principle is applicable to microscopic as well as macroscopic particle d. Heisenberg uncertainty principle is ruled out the concept of definite trajectories around the nucleus.

Select the correct statement(s) about Uncertainty principle. a. The product of uncertainty in momentum in position is always constant b. This principle can explain why electron cannot exist in nucleus c. This principle is applicable to microscopic as well as macroscopic particle d. Heisenberg uncertainty principle is ruled out the concept of definite trajectories around the nucleus.

Select the correct statement(s) about Uncertainty principle.
a. The product of uncertainty in momentum in position is always constant
b. This principle can explain why electron cannot exist in nucleus
c. This principle is applicable to microscopic as well as macroscopic particle
d. Heisenberg uncertainty principle is ruled out the concept of definite trajectories around the nucleus.

Key Concepts

Breakdown of Definite Classical Trajectories

Unlike classical mechanics where particles follow well-defined trajectories, quantum mechanics replaces these trajectories with probability distributions. The uncertainty principle eliminates the possibility of ascribing a definite path to a particle, reflecting the probabilistic nature of quantum phenomena.

Quantum Confinement Effects

Quantum confinement refers to the phenomenon where the spatial restriction of a particle, such as an electron, leads to an increased uncertainty in its momentum and consequently higher kinetic energy. This concept is important in understanding why particles like electrons cannot be arbitrarily confined, as attempting to confine them to extremely small regions would require correspondingly large momentum uncertainty.

Scale-Dependence of Quantum Effects

Quantum uncertainty is most prominently observed in microscopic systems where the effects are significant due to the small scales involved. In contrast, for macroscopic objects, these quantum uncertainties become negligible, making classical descriptions more applicable even though the underlying principles remain universally valid.

Heisenberg Uncertainty Principle

This principle is a cornerstone of quantum mechanics, stating that certain pairs of observables, such as position and momentum, have a fundamental limit to the precision with which they can be simultaneously measured. The mathematical formulation is usually given by the inequality ?x · ?p ? ?/2, emphasizing that the more precisely one observable is known, the less precisely the other can be determined.

Position-Momentum Uncertainty Relation

At the heart of the uncertainty principle is the relationship between the uncertainties in position and momentum. This relation highlights that the product of these uncertainties cannot fall below a specified limit. It is the quantitative expression of the inherent limitations imposed by quantum mechanics on measuring conjugate variables simultaneously.

Please give Ace some feedback