Chemistry · Dual nature of matter, de Broglie's relationship, Heisenberg uncertainty principle
Uncertainity in position of a particle of in space is Determine uncertainity in
Uncertainity in position of a particle of \( 25 \mathrm{g} \) in space is \( 10^{-15} \mathrm{m} . \) Determine uncertainity in velocity \( \left(\mathrm{m} \mathrm{sec}^{-1}\right) \) in it. (plank's constant, \( \boldsymbol{h}=\mathbf{6 . 6} \times \mathbf{1 0}^{-\mathbf{3 4}} \mathbf{J s} \) )
- A. \( 2.1 \times 10^{-18} \)
- B. \( 1.2 \times 10^{-18} \)
- C. \( 1.8 \times 10^{-18} \)
- D. \( 2.5 \times 10^{-18} \)
Step-by-step solution
Heisenberg's uncertainty principle: Δx·Δp ≥ h/(4π). Here Δp = m·Δv. So Δv ≥ h/(4π·m·Δx). Plugging values: h=6.6×10^{-34} Js, m=25 g=0.025 kg, Δx=10^{-15} m, π≈3.14. Compute denominator: 4π·m·Δx = 4×3.14×0.025×10^{-15} ≈ 3.14×10^{-16}. Then Δv ≥ 6.6×10^{-34} / (3.14×10^{-16}) ≈ 2.1×10^{-18} m/s.
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