Question

An electron has speed 6.6/10^-4 m/s with an accuracy 0.01% .calculate uncertainty in the position of the electron ?

Answer 1

Explanation:

mass of electron, m = 9.1* 10–³¹ kg

accuracy in velocity = 0.01%

inaccuracy or uncertainty in velocity, ∆v = 6.6*10⁴ * (100–99.99)%

= 6.59*10⁴ m/s

now if ∆x is uncertainty in position , then according to Heisenberg's uncertainty Principle:

∆x*m∆v ≥ h/4π

(h Planck's constant = 6.626*10–34Kgm²/s)

or, ∆x = h/(4π*m∆v)

or, ∆x = 8.79*10^–10 m

= 8.79 Å