UncategorizedThe uncertainties in the velocities of two particles A and B are 0.05 and 0.02m.sec−1respectively. The mass of B is five times to that of mass A. What is the ratio of uncertainties (ΔxAΔxB) in their positions

The uncertainties in the velocities of two particles A and B are 0.05 and 0.02m.sec1respectively. The mass of B is five times to that of mass A. What is the ratio of uncertainties (ΔxAΔxB) in their positions

  1. A

    2

  2. B

    0.25

  3. C

    4

  4. D

    1

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    Solution:

    Heisenberg uncertainty principle,

    Δx.Δv=h4πm

    From given data ,

    vA=0.05 m.sec1

    vB=5m.sec1

    Mass of A is equal to mA=m

    Then mass of B is equal to 5 times than mass of A.

    So, mB=5m

    The ratio of uncertainties of A and B is

    ΔxAΔxB=mBmA×ΔvBΔvA                  

    ΔxAΔxB=5mm×0.020.05=2

              

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