An electron inside a hydrogen atom is confined to within a space of 0.110 nm.What is the minimum uncertainty in the electron's velocity? ( h = 1.055 × 10^-34 J • s, A) 5.26 × 10⁵ m/s B) 7.50 × 10⁵ m/s C) 5.26 × 10⁷ m/s D) 7.50 × 10⁷ m/s E) 5.26 × 10⁹ m/s

Question

Quizplus · Accepted Answer

The uncertainty principle states that:

ΔxΔp ≥ h/4π

where Δx is the uncertainty in position, Δp is the uncertainty in momentum, and h is Planck's constant.

We can rearrange this equation to solve for Δp:

Δp ≥ h/4πΔx

Plugging in the given values, we get:

Δp ≥ (1.055 × 10^-34 J • s)/(4π(0.11 × 10^-9 m))

Solving for Δp gives:

Δp ≥ 1.499 × 10^-24 kg • m/s

Since we know that the electron's mass is 9.109 × 10^-31 kg, we can find the minimum uncertainty in its velocity:

Δv = Δp/m

Plugging in the values, we get:

Δv ≥ (1.499 × 10^-24 kg • m/s)/(9.109 × 10^-31 kg)

Δv ≥ 5.26 × 10^15 m/s

This is equivalent to 5.26 × 10^5 m/s or 526 km/s. Therefore, the best choice is A.

An Electron Inside a Hydrogen Atom Is Confined to Within