Question

State Heisenberg’s uncertainty principle.

Answer 1

In quantum mechanics, Heisenberg’s uncertainty principle is one of the most important theories that describe why it is not possible to determine more than value variables at the same time.

Complete step by step answer:
Heisenberg’s uncertainty principle states that it is not possible to determine or measure with high accuracy, both the momentum and the location of a particle at the same time. This principle is established on the dual nature of matter. However, this principle can be neglected while dealing with the location and velocity of the large masses (macroscopic world), it holds pronounced value in the microscopic world or quantum world. The mass of the atomic and subatomic particles are extremely small, so any change in the accuracy of the location will be accompanied by a change in the uncertainty related with the velocity of the particle.
If $\Delta x$ is the error in measurement of location of the particle and $\Delta p$ is the error in measurement of its momentum, then
$\Delta x \cdot \Delta p \ge \dfrac{h}{{4\pi }}$
We know that the momentum is $p = mv$, we can write the above equation as,
$\Delta x \cdot \left( {m\Delta v} \right) \ge \dfrac{h}{{4\pi }}$
$\Delta x \cdot \Delta v \ge \dfrac{h}{{4\pi m}}$
Here, $\Delta v$ is the error in measurement of velocity of the particle.

Note: The Bohr model is failed because of the Heisenberg’s uncertainty principle because Bohr postulates that the electrons, which is a quantum particle, moves with a constant velocity around the nucleus in a fixed path. So, according to this, the position or location and momentum can be determined at the same time and this contradicts the Heisenberg’s uncertainty principle.