Question

Assume we can localize a particle of an uncertainty of 0.5 nm. What will be the resulting uncertainty in the particle's momentum (in kg m/s)?

Answer 1

To determine the uncertainty in a particle's momentum when the uncertainty in position is 0.5 nm, we apply the Heisenberg Uncertainty Principle, specifically ΔxΔp ≥ ħ/4π. Substituting the given values into this equation allows us to calculate the minimum uncertainty in the particle's momentum in kg m/s.

Step-by-step explanation:

The Heisenberg Uncertainty Principle provides a fundamental limit to the precision with which certain pairs of physical properties, such as position and momentum, can be known simultaneously. To find the resulting uncertainty in the particle's momentum when the uncertainty in position is given as 0.5 nm, we use the formula ΔxΔp ≥ ħ/4π, where ħ (h-bar) is the reduced Planck constant (ħ = h/2π), and Δx and Δp are the uncertainties in position and momentum, respectively.

Using the provided uncertainty in position (Δx = 0.5 nm = 0.5 × 10-9 m) and the value of ħ as 1.055 × 10-34 kg m2/s, we can rearrange the equation to solve for Δp:

ΔxΔp ≥ ħ/4π

Δp ≥ (ħ/4π) / Δx

Substitute the values:

Δp ≥ (1.055 × 10-34 kg m2/s) / (4π × 0.5 × 10-9 m)

After performing the calculation, we obtain the value for the uncertainty in momentum, which is in the unit of kilograms meters per second (kg m/s).