Question

If the position of a chlorine ion in a membrane is measured to an accuracy of 2.00 µm, what is its minimum uncertainty in velocity, given its mass is 5.86 ✕ 10^-26 kg?
  m/s
(b) If the ion has this velocity, what is its kinetic energy in eV? (Compare this with typical molecular binding energies of about 5 eV.)
eV

Answer 1

Applying Uncertainty Principle

(delta X) (delta V) >= (h / 4 m pi)

Given delta X = 2 x 10^-6 m

m = 5.86 x 10^-26 kg

h = 6.626 x 10^-34

(delta V) > = ( h / ( 4 pi m delta X )

delta V >= ( 6.626 x 10^-34 / ( 4 x pi x 5.86 x 10^-26 x 2 x 10^-6))

delta V >= 0.00044989 m/s

(b) velocity = v = 0.00044989 m/s

Kinetic energy = 0.5 m v^2 = 0.5 x 5.86 x 10^-26 x (0.00044989)^2 = 5.93 x 10^-33 J

= 5.93 x 10^-33 / (1.6 x 10^-19) = 3.706 x 10^-14 eV

Ion's kinetic energy is munch lower compared to typical molecular binding energies