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The uncertainty in the momentum of a par...

The uncertainty in the momentum of a particle is `2.2 xx 10^(-4) g cm s^(-1)`. With what accuracy can its position be deterimed ? `(h = 6.626 xx 10^(-27) " erg" s)`

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To solve the problem of determining the accuracy with which the position of a particle can be determined given the uncertainty in its momentum, we will use the Heisenberg Uncertainty Principle. Here’s a step-by-step solution: ### Step 1: Understand the Heisenberg Uncertainty Principle The Heisenberg Uncertainty Principle states that the product of the uncertainties in position (Δx) and momentum (Δp) of a particle is greater than or equal to a constant value: \[ \Delta p \cdot \Delta x \geq \frac{h}{4\pi} \] where \( h \) is Planck's constant. ...
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Knowledge Check

  • The uncertainty in the momentum of a particle is 3.3 xx10^(-2) kg ms^(-1) the uncertainty in its position will be

    A
    `1.6 xx 10^(-33)`m
    B
    `1.6 xx 10^(-32)`m
    C
    `1.6 xx 10^(-30)`m
    D
    `1.6 xx 10^(-29)`m
  • The uncertainty in the velocity of a particle of mass 6.626 xx 10^(-31) kg is 1 xx 10^6 ms^(-1) . What is the uncertainty in its position (in nm) ? (h = 6.626 xx 10^(-34) Js)

    A
    `(1/(2pi))`
    B
    `((2.5)/(pi))`
    C
    `(4/(pi))`
    D
    `(1/(4pi))`
  • The uncertainity in the momentum of an electron is 1.0xx10^(-5)"kg m s"^(-1) . The uncertainity in its position will be: (h=6.626xx10^(-34)Js)

    A
    `1.05 xx 10^(-28)m`
    B
    `1.05 xx 10^(-26)m`
    C
    `5.27xx10^(-30)m`
    D
    `5.25xx10^(-28)m`
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    The uncertainty in the velocity of particle of mass 6.626xx10^(-28) kg is 10^(6) m/sec. What is the uncertaintly in its position in nm?

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