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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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