Question

A proton is confined to a space 1 fm wide (about the size of an atomic nucleus). What’s the minimum uncertainty in its velocity?

Answer 1

Uncertainty in position = Δx = if m 1 × 10-15m

mass of proton = m = 1.67 × 10-27 kg

By heignberg uncertainty principle

Δx Δp = h/2π  

 

∴ {Δp → uncertainty in momentum, n = 6.626 × 10-34 J∙s, ΔV → uncertainty in velocity}

 

⇒ Δp = h/2πΔx = 6.626 × 10-34/2π × 10-15

⇒ Δp = 1.05456 × 10-19 kgm/s

 

As Δp = mΔV ⇒ ΔV = Δp/m = 1.0546 × 10-19/1.67 × 10-27

⇒ ΔV = 0.631 × 108 = 6.31 × 107 m/s

ΔV = 0.631 × 108 = 6.31 × 107 m/s