Question

Calculate the uncertainty in position of a dust particle with mass equal to 1 mg if the uncertainty in its velocity is 5.5 x 10 -20 m/s.

Answer 1

Mass of dust particle= 1 x 10⁻³/1 x 10⁻³/1 = 10⁻⁶kg
change in velocity= 5.5 x 10⁻²⁰
h= 6.623 x 10⁻³⁴
x= 22/7

Δx⇒ mΔv= h/ 4π
Δx= h/ mΔv4π

= 6.623 x 10⁻³⁴ x 7/ 4 x 22 x 10⁻⁶ x 5.5 x 10⁻²⁰
Δx= 9.58 x 10⁻¹⁰ m

Answer 2

Answer:

Δx=9.6×10 −10m

Explanation:

Δu.Δx= 4πm/h (Heisenberg uncertainty principle equation)

Uncertainty principle says that we cannot measure the position and the momentum of the particle with absolute precision.

(Given Δu=5.5×10 −20 ms  −1

;m(mass of the dust particle)=1×10 −6 kg)

Δu.Δx= (5.5×10−20)×Δx

= (6.626×10 −34)/(4x3.14 ×10 −6)

 Δx( change in position of dust particle) =9.6×10 −10m

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