Question

What is the uncertainty in the position of an electron moving at 9.00 × 10 6 m/s with an uncertainty of Δ v = 0.01 × 10 6 m/s ?

Answer 1

Answer:

The uncertainty in the position of the electron is 5.787 nm

Explanation:

Δx ≥ h/(4πmΔv)

where;

h is Planck's constant and m is the mass of the object.

Planck's constant = 6.626 X 10⁻³⁴

The mass of an electron is 9.11 x 10⁻³¹kg.

Δv is the change in velocity  0.01 × 10⁶ m/s

Δx ≥ h/(4π*mΔv)  = (6.626 X 10⁻³⁴)/(4π*9.11 x 10⁻³¹ *0.01 × 10⁶)

Δx ≥ 5.787 X 10⁻⁹ m

Δx ≥ 5.787 nm

Therefore, the uncertainty in the position of the electron is 5.787 nm