Question

PROBLEN 60. Calculate the uncertainty in the position of an
electron if the uncertainty in its velocity is 5.7 x 10^5m/s
( h = 6.6 x 10-kgm^2s^-1 ).mass of electron = 9.1 x 10-31 kg
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Answer 1

Answer:

±10⁻¹⁰m

Explanation:

Velocity (Δv) =5.7×10⁵ms⁻¹

Mass of electron (m) =9.1×10⁻³¹ kg

Planck's constant (h) = 6.6×10⁻³⁴kg m²s⁻¹

Substituting these values in the equation of heisenberg's uncertainty principle,

Δx * (m * Δv) = h / 4π

so

Δx = h / (4π × m × Δv)

=6.6 × 10⁻³⁴kg m²s⁻¹/(4 × 22/7 × 9.1×10⁻³¹ kg × 5.7×10⁵ ms⁻¹)

=1.0*10⁻¹⁰m

Uncertainty in position =±10⁻¹⁰ m