Calculate the uncertainty in the position of (a) an electron moving at a speed of 13.00 { 0.012 * 105 m/s

Key Concepts

Heisenberg Uncertainty Principle

The Heisenberg Uncertainty Principle states that it is impossible to simultaneously know both the exact position and momentum of a particle. This principle is fundamental in quantum mechanics and implies that the more precisely one property is measured, the less precisely the other can be controlled or known. For an electron, this means that as we try to measure its position more accurately, the uncertainty in its momentum increases.

Momentum

Momentum is defined as the product of an object's mass and its velocity. In the context of quantum mechanics, the momentum of a particle like an electron is crucial for applying the Heisenberg Uncertainty Principle. The momentum can be calculated using the formula p = mv, where p is momentum, m is mass, and v is velocity. Understanding momentum is essential for determining the uncertainty in position.

Uncertainty Calculation

To calculate the uncertainty in position (Δx) of a particle, one can use the relationship derived from the Heisenberg Uncertainty Principle, which is Δx * Δp ≥ ħ/2, where Δp is the uncertainty in momentum and ħ is the reduced Planck's constant. By determining the uncertainty in momentum from the particle's velocity and mass, one can rearrange this equation to find the uncertainty in position, which is critical for solving the given problem.