The uncertainties in the velocities of two particles A and B are 0.05 and 0.02 ms^-1 respectively. The mass of B is five times to that of mass A. What is the ratio of uncertainties ( $(∆ x_{A} / ∆ x_{B}) in their positions$ ?
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Question

The uncertainties in the velocities of two particles A and B are 0.05 and 0.02 ms^-1 respectively. The mass of B is five times to that of mass A. What is the ratio of uncertainties ( $(∆ x_{A} / ∆ x_{B}) in their positions$ ?

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Infinity Learn · Accepted Answer

According to Heisenberg,Δx×m×Δ$$v=h4$$$$π$$where, Δ$$x=$$ uncertainty in position $$m=$$ mass of particleΔ$$v=$$ uncertainty in velocity According to question,ΔxA×m×$$0.05=h4$$πΔxB×$$5m$$×$$0.02=h4$$$$π$$Divide Eq. $$()$$ by Eq. (i), then⇒ ΔxAΔ$$xB=5m$$×$$0.02m$$×$$0.05=2$$ or ΔxAΔ$$xB=2$$

The uncertainties in the velocities of two particles A and B are 0.05 and 0.02 ms^-1 respectively. The mass of B is five times to that of mass A. What is the ratio of uncertainties $({Δx}_{A} / {Δx}_{B})$ in their positions?

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The uncertainties in the velocities of two particles A and B are 0.05 and 0.02 ms-1 respectively. The mass of B is five times to that of mass A. What is the ratio of uncertainties ΔxA/ΔxB in their positions?

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The uncertainties in the velocities of two particles A and B are 0.05 and 0.02 ms^-1 respectively. The mass of B is five times to that of mass A. What is the ratio of uncertainties $({Δx}_{A} / {Δx}_{B})$ in their positions?