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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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 $({Δx}_{A} / {Δx}_{B})$ in their positions?

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Infinity Learn · Accepted Answer

According to Heisenberg,∆x ×m×∆v $$=$$ $$h4$$$$π$$where, ∆x $$=$$ uncertainty in position              m $$=$$ mass of particle             ∆v $$=$$ uncertainty in velocityAccording to question,∆xA×m×$$0.05$$ $$=$$ $$h4$$π∆xB×$$5m$$×$$0.02$$ $$=$$ $$h4$$$$π$$Divide Eq.(i) by Eq.(ii), then∆xA×m×$$0.05$$∆xB×$$5m$$×$$0.02$$ $$=$$ $$1$$⇒∆xA∆xB  $$=$$ $$5m$$×$$0.02m$$×$$0.05$$ $$=$$ $$2or$$ ∆xA∆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 ( $(∆ x_{A} / ∆ x_{B}) in their positions$ ?

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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 ((∆xA/∆xB) in their positions?

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Ready to Test Your Skills?

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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 ( $(∆ x_{A} / ∆ x_{B}) in their positions$ ?