Chapter 5, Problem 5.2P

Interpretation Introduction

Interpretation:

Greatest precision for the alpha particle has to be calculated.

Concept Introduction:

Heisenberg uncertainty principle states that it impossible to measure the exact position and the momentum of a particle at the same time.  This can be expressed mathematically as shown below.

    $(\Delta x)(\Delta p)\ge \frac{h}{4\pi }$

Where,

    $h$ is the Planck’s constant.

    $\Delta x$ is the uncertainty associated with position.

    $\Delta p$ is the uncertainty associated with momentum.

It is known that the product of mass and velocity is the momentum of the particle.  This can be expressed as shown below.

    $\Delta p=m\Delta v$

Therefore, Heisenberg’s uncertainty principle can also be expressed as shown below.

    $(\Delta x)(m\Delta v)\ge \frac{h}{4\pi }$