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Ans. Heisenberg’s Uncertainty Principle is a fundamental principle of quantum mechanics, proposed by physicist Werner Heisenberg in 1927. It states that certain pairs of physical properties, such as the position and momentum of a particle, cannot be simultaneously measured with arbitrary precision.
Q.2 : Why is it called the "Uncertainty Principle"?
Ans. It is called the Uncertainty Principle because it implies that there are inherent limits to the precision with which certain pairs of physical properties of a particle can be known simultaneously. In other words, there is inherent uncertainty in our ability to measure these properties simultaneously.
Q.3 : What does the Uncertainty Principle imply about the behaviour of particles?
Ans. The Uncertainty Principle implies that at the quantum level, particles exhibit inherent indeterminacy in their behaviour. This means that we cannot predict with certainty both the position and momentum of a particle simultaneously. Instead, we can only determine the probability distribution of these properties.
Q.4 : How does the Uncertainty Principle challenge classical physics?
Ans. The Uncertainty Principle challenges classical physics, which assumes that the properties of particles can be measured with arbitrary precision. In contrast, the Uncertainty Principle imposes limits on our ability to precisely measure certain pairs of physical properties of particles.
Q.5 : What are some examples of pairs of properties affected by the Uncertainty Principle?
Ans. Examples of pairs of properties affected by the Uncertainty Principle include the position and momentum of a particle, the energy and time of a quantum event, and the angular momentum and angular position of a rotating object.
Q.6 : How does the Uncertainty Principle impact experimental measurements?
Ans. The Uncertainty Principle imposes limitations on the precision of measurements in quantum mechanics. It means that there is a trade-off between the precision with which certain pairs of properties can be measured. For example, the more precisely we measure the position of a particle, the less precisely we can measure its momentum, and vice versa.
Q.7 : Can the Uncertainty Principle be overcome with more advanced measurement techniques?
Ans. No, the Uncertainty Principle is a fundamental principle of quantum mechanics and cannot be overcome with more advanced measurement techniques. It is not a limitation of our measuring instruments but rather a fundamental aspect of the behaviour of particles at the quantum level.
Q.8 : What are the real-life examples illustrating the Uncertainty Principle?
Ans. One real-life example illustrating the Uncertainty Principle is the measurement of the position and momentum of an electron in an atom. According to the Uncertainty Principle, the more precisely we measure the position of the electron, the less precisely we can measure its momentum, and vice versa. This inherent uncertainty in the measurement of these properties is a fundamental aspect of quantum mechanics.
Quantum Mechanical Model of An Atom, Heisenberg’s Uncertainty Principle
Quantum Mechanical Model of An Atom : Discover the Quantum Mechanical Model of an Atom, a fundamental theory in quantum physics. Learn how electrons exist in probability clouds, not fixed orbits, defined by quantum numbers. Explore concepts like wave-particle duality, uncertainty principle, and electron configuration in this concise overview.
Shrivastav 30 May, 2024
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Quantum Mechanical Model of An Atom :
Welcome, fellow explorers of science! Have you ever wondered what lies at the heart of the tiny atoms that make up everything around us? Well, buckle up as we embark on an exhilarating journey into the quantum realm to unravel the mysteries of atomic structure. In this article, we'll delve into the fascinating concept of Heisenberg’s Uncertainty Principle and its role in shaping our understanding of the quantum mechanical model of an atom. So, let's dive in and discover the hidden wonders of the atomic world.
Understanding the Quantum Mechanical Model of an Atom
Before we delve into Heisenberg’s Uncertainty Principle, let's first understand the quantum mechanical model of an atom. Imagine the atom as a miniature solar system, with a nucleus at the centre composed of protons and neutrons, and electrons orbiting around it in specific energy levels or "shells." This model, developed through the contributions of scientists like Niels Bohr and Louis de Broglie, revolutionized our understanding of atomic structure..
Unlike the classical model of the atom, which depicts electrons moving in well-defined orbits, the quantum mechanical model describes electrons as existing in regions of space called orbitals. These orbitals represent the probability distribution of finding an electron at a given location around the nucleus. This wave-like behaviour of electrons is a fundamental principle of quantum mechanics.
Heisenberg’s Uncertainty Principle
Now, let's turn our attention to Heisenberg’s Uncertainty Principle, proposed by the renowned physicist Werner Heisenberg in 1927. This principle is a cornerstone of quantum mechanics and has profound implications for our understanding of the behaviour of particles on the atomic and subatomic scales.
Heisenberg’s Uncertainty Principle states that it is impossible to simultaneously measure certain pairs of physical properties of a particle, such as its position and momentum, with arbitrary precision. In other words, the more precisely we know the position of a particle, the less precisely we can know its momentum, and vice versa.
The uncertainty in measurement of position,
and the uncertainty in momentum
are related by Heisenberg’s relationship as
Where h is Planck’s constant.
(i)
When
(ii)
When
So, if the position is known quite accurately, i.e.,
is very small,
becomes large and vice-versa.
Explanation Of Heisenberg’s Uncertainty Principle
Suppose we attempt to measure both the position and momentum of an electron. To pin point the position of the electron we have to use light so that the photon of light strikes the electron and the reflected photon is seen in the microscope. As a result of the hitting, the position as well as the velocity of the electron are disturbed.
Significance of Uncertainty Principle
It rules out the existence of definite paths or trajectories of electrons as stated in Bohr’s Model.
Important Note :
The effect of the Heisenberg Uncertainty Principle is significant only for the motion of microscopic objects and is negligible for that of macroscopic objects.
Significance of Uncertainty Principle Solved Example
1.
Calculate the uncertainty in the position of a particle when the uncertainty in momentum is
(a) 1 × 10
–3
g cm s
–1
(b) zero
Sol.:
(a)
Given
= 1 × 10
–3
g cm s
–1
, h = 6.62 × 10
–27
erg s,
= 3.142
According to Heisenberg’s uncertainty principle
(b)
When the value of
the value of
will be infinity.
2.
The uncertainty in position and velocity of a particle are 10
–10
m and 5.27 × 10
–24
ms
–1
respectively.
Calculate the mass of the particle (h = 6.625 × 10
–34
joule second)
Sol.:
According to Heisenberg’s uncertainty principle,
3.
Calculate the uncertainty in velocity of a cricket ball of mass 150 g if the uncertainty in its position is of the order of 1Å (h = 6.6 × 10
–34
kg m
2
s
–1
).
Sol.:
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