uncertainty position electron velocity 417 km/s

Find the uncertainty in position (in nm)

associated with an electron

that is moving with a velocity of 417 km/s.

The uncertainty in the velocity is 5.00%.

The electron rest mass is 9.11×10^(-31) kg.

---------------------------------------------------

[참고] 하이젠베르크의 불확정성 원리

Heisenberg’s uncertainty principle

Δv = (417 km/s) (1000 m / 1 km) (5.00/100)

= (417) (1000) (5.00/100)

= 20850 m/s

(Δx) × (ΔP) ≧ (h / 4π)

> h = 6.626×10^(-34) kg•m^2/s

Δx = h / (m × Δv × 4π)

= (6.626×10^(-34)) / ((9.11×10^(-31)) × 20850 × 4π)

= 2.78×10^(-9) m

(2.78×10^(-9) m) (10^9 nm / 1 m) = 2.78 nm

답: 2.78 nm

[참고] Δx를 한 번에 계산하면,

(6.626×10^(-34)) / ((9.11×10^(-31)) × 417000×(5.00/100) × 4π)

[키워드] 하이젠 기준