Question

A particle has a mass of 0.002 kg and uncertainty in its velocity is 9.2 × 10⁻⁶ m/s, then uncertainty in position is ≥ ____________.

(h = 6.6 × 10⁻³⁴ J s)

Options

• 2.86 × 10⁻²⁸ m

• 2.86 × 10⁻²⁹ m

• 2.86 × 10⁻³⁰ m

• 2.86 × 10⁻³⁴ m

Answer 1

A particle has a mass of 0.002 kg and uncertainty in its velocity is 9.2 × 10⁻⁶ m/s, then uncertainty in position is ≥ 2.86 × 10⁻²⁹ m.

Explanation:

According to Heisenberg's uncertainty principle, `Δ"x".Δ"v"_"x" ≥ "h"/(4π"m")`

∴ `Δ"x" ≥ "h"/(4π"m" xx Δ"v"_"x")`

`Δ"x" ≥ (6.6 xx 10^-34)/(4 xx 3.14 xx 0.002 xx 9.2 xx 10^-6)`

`Δ"x" ≥ 2.86 xx 10^-29  "m"`