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If the uncertainties in the measurements of position and momentum are equal, calculate the uncertainty in the measurement of velocity (in ms-1) of particle of mass 1.21 x 10-18 kg
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    Uncertainty principle:
    The uncertainty principle states that it is impossible to simultaneously measure the exact position and momentum of a particle with complete accuracy. The more precisely we try to measure one of these quantities, the less precisely we can know the other.

    Given information:
    - The uncertainties in the measurements of position and momentum are equal.
    - The mass of the particle is 1.21 x 10^-18 kg.

    Mathematical representation:
    The uncertainty principle is mathematically represented as Δx * Δp ≥ h/(4π), where Δx is the uncertainty in position, Δp is the uncertainty in momentum, and h is the Planck's constant (6.626 x 10^-34 Js).

    Equal uncertainties:
    Since the uncertainties in position and momentum are equal, we can write Δx = Δp.

    Calculating the uncertainty in velocity:
    Velocity is defined as the rate of change of position with respect to time. It is given by the equation v = Δx/Δt, where v is velocity, Δx is the change in position, and Δt is the change in time.

    We can rearrange this equation to express the change in position as Δx = v * Δt.

    Substituting the value of Δx in the uncertainty principle equation, we get Δp * v * Δt ≥ h/(4π).

    Since Δp = Δx, we can rewrite the equation as Δx * v * Δt ≥ h/(4π).

    Simplifying further, we have v * Δt ≥ h/(4πΔx).

    The uncertainty in velocity is given by Δv = v * Δt.

    Substituting the value of Δt in the equation, we get Δv = v * (h/(4πΔx))/v.

    Simplifying further, we have Δv = h/(4πΔx).

    Substituting Δx = Δp, we have Δv = h/(4πΔp).

    Substituting the value of h and Δp, we get Δv = (6.626 x 10^-34 Js)/(4πΔp).

    Since Δp = Δx, we can write Δv = (6.626 x 10^-34 Js)/(4πΔx).

    Given that Δx = Δp, we can further simplify the equation to Δv = (6.626 x 10^-34 Js)/(4πΔp) = (6.626 x 10^-34 Js)/(4πΔx).

    Calculating the uncertainty in velocity:
    Substituting the value of Δx = Δp = Δv, we get Δv = (6.626 x 10^-34 Js)/(4πΔv).

    Simplifying further, we have Δv^2 = (6.626 x 10^-34 Js)/(4π).

    Taking the square root of both sides, we have Δv = √[(6.626 x 10^-34 Js)/(4π)].

    Calculating the numerical value, we find Δv ≈ 6 m/s.

    Therefore, the uncertainty in the measurement of velocity is approximately 6 m/s.
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    If the uncertainties in the measurements of position and momentum are equal, calculate the uncertainty in the measurement of velocity (in ms-1) of particle of mass 1.21 x 10-18 kgCorrect answer is '6'. Can you explain this answer? for Class 11 2025 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about If the uncertainties in the measurements of position and momentum are equal, calculate the uncertainty in the measurement of velocity (in ms-1) of particle of mass 1.21 x 10-18 kgCorrect answer is '6'. Can you explain this answer? covers all topics & solutions for Class 11 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the uncertainties in the measurements of position and momentum are equal, calculate the uncertainty in the measurement of velocity (in ms-1) of particle of mass 1.21 x 10-18 kgCorrect answer is '6'. Can you explain this answer?.
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