Question

Heisenberg's uncertainty principle rules out the exact simultaneous measurement of:
A. probability and intensity
B. energy and velocity
C. charge density and radius
D. Position and velocity

Answer 1

In quantum mechanics the uncertainty is a variety of mathematical inequalities. It’s impossible to simultaneously determine the position velocity of small microscope particles such as electrons, protons or neutrons with accuracy. This is known as Heisenberg’s uncertainty principle.

Complete step by step answer:
-The uncertainty principle is also known as the Heisenberg uncertainty principle. It is also known as indeterminacy principle. In $1927$ the German physicist Werner Heisenberg stated that the position and the velocity of an object both cannot be measured exactly at the same time, if even in the theory.
The very concept of the exact position and the exact velocity together .In fact it had no meaning in nature.
-The ordinary experience provides no clues of this principle.It is easy to measure both the position and the velocity of an automobile because the uncertainties implied by this principle for all the ordinary objects that are too small to be observed.
-The complete rule stipulates that the product of the uncertainties in the position and the velocity to or greater than the tiny physical quantity or constant ($\dfrac{h}{{4\pi }}$) where $h$ is planck's constant about ($6.6 \times {10^{35}}$) joule second.
-Only for the exceedingly small masses of atom and subatomic particles does the product of the uncertainties become significant.
So, the correct answer is “Option D”.

Note:
The uncertainty principle says that we cannot measure the position ($x$) and the momentum ($p$) of a particle with the absolute precision. The more accurately we know one of these values and the less accurately we know the other. It states that the position and the velocity of an object both cannot be measured exactly at the same, if even in the theory.
Mathematically it is represented as,
$\Delta x.\Delta p \geqslant \dfrac{h}{{4\pi }}$
$\Delta x$ is uncertainty in position.
$\Delta p = m\Delta v$ is uncertainty in momentum.