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Calculate the uncertainty in the velocit...

Calculate the uncertainty in the velocity of a particle of mass `1.1xx10^(-27)` kg if the uncertainty in the uncertainty in its position is `3xx10^(-10)cm`.

Text Solution

Verified by Experts

The correct Answer is:
`1.6xx10^(4) m s^(-1)`
According to uncertainty principle,
`Deltax*m Deltav=(h)/(4pi) or Deltav=(h)/(4pimDeltax)`
`Deltax=3xx10^(-10)=3xx10^(-12)m, m=1.1xx10^(-27) "kg" , pr=3.143`,
`h=6.626xx10^(-34) "kg"m^(2)s^(-1)"`
`Deltav=((6.626xx10^(-34)"kg"m^(2)s^(-1)))/(4xx3.143xx(1.1xx10^(-27)"kg")xx(3xx10^(-12)m))=1.6xx10^(4)ms^(-1)`.
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Knowledge Check

  • 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?

    A
    `(1)/(2pi)`
    B
    `(2.5)/(pi)`
    C
    `(4)/(pi)`
    D
    `(1)/(4pi)`

  • 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?

    A
    `(1)/(2pi)`
    B
    `(2.5)/(pi)`
    C
    `(4)/(pi)`
    D
    `(1)/(4pi)`

  • Calculate the minimum uncertainty in velocity of a particle of mass 1.1 xx 10^-27 kg if uncertainty in its position is 3 xx 10^-10 cm .

    A
    `1.5 xx 10^-4 m`
    B
    `2.5 xx 10^-4 m`
    C
    `3.5 xx 10^-4 m`
    D
    `4.5 xx 10^-4 m`

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