Question

Identify the statement which best defines the uncertainty principle?
F. We cannot know for certain when any given radioactive particle will undergo decay
G. We cannot know both the momenta m and the position of a particle at the same time
H. The laws of physics are the same in all intertie reference frames
I. Light exhibits both wave and particle properties
J. An unobserved particle can be in two places at the same time

Answer 1

Hint: A central concept in quantum mechanics is Heisenberg’s theory of uncertainty. Rather
loosely, it states that if we know anything about where a particle is located, we know nothing
about its momentum and vice versa.
Heisenberg uncertainty principle: The principle of uncertainty (also known as the Heisenberg
uncertainty principle) is one of a variety of mathematical inequalities which assert a fundamental
limit to the precision with which values for certain pairs of particle physical quantities, such as
position, x, and momentum, p, can be predicted from the initial conditions. Such variable pairs
are known as complementary variables or canonically conjugate variables, and the concept of
ambiguity, depending on definition, restricts the degree to which these conjugate properties
preserve their approximate significance, since the mathematical structure of quantum physics
does not accept the notion of at the same time well-defined conjugate properties expressed by a
single value. The theory of uncertainty means that the value of a quantity can usually not be
calculated with absolute certainty, even though all the initial conditions are stated.
The Heisenberg theory of uncertainty states that the exact momentum and the exact position of
the particle at the same instant cannot be determined.
If we specify the particle's position value, then the value of its velocity (momentum) and vice-
versa would be highly uncertain.
From to uncertainty principle, $\Delta p.\Delta x \ge \dfrac{h}{{4\pi }}$
We observed that we cannot know both the momenta m and the position of a particle at the same
time.
Hence the required answer is B.
Note: In this solution, we observed the Heisenberg uncertainty principle; this principle states that
the exact momentum and the exact position of the particle at the same instant cannot be
determined.