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QJEEM02Ch0151: JEE Main 2002 Chemistry - Class 11 JEEM02Ch0151 Solution: Uncertainty in position of a minute particle of mass 25 g in…

Uncertainty in position of a minute particle of mass 25 g in space is 10-5 m. What is the uncertainty in its velocity (in ms-1) (h = 6.6 × 10-34 Js)

Multiple Choice Options

  • A 2.4 × 10-34
  • B 0.5 × 10-34
  • C 2.1 × 10-28
  • D 0.5 × 10-23

Step-by-Step Verified Solution

According to Hysenberg's Uncertainty Principal </mo></mrow><mimathvariant="normal">Δ</mi><mi>x</mi><mo>.</mo><mimathvariant="normal">Δ</mi><mi>p</mi><mo>≥</mo><mrowdata−mjx−texclass="ORD"><mfrac><mi>h</mi><mrowdata−mjx−texclass="ORD"><mn>4</mn><mi>π</mi></mrow></mfrac></mrow></math></mjx−assistive−mml></mjx−container></mjx−assistive−mml></mjx−container></mo></mrow><mi mathvariant="normal">Δ</mi><mi>x</mi><mo>.</mo><mi mathvariant="normal">Δ</mi><mi>p</mi><mo>≥</mo><mrow data-mjx-texclass="ORD"><mfrac><mi>h</mi><mrow data-mjx-texclass="ORD"><mn>4</mn><mi>π</mi></mrow></mfrac></mrow></math></mjx-assistive-mml></mjx-container></mjx-assistive-mml></mjx-container> Where Δx is uncertainty in position and Δp is uncertainty in momentum and as in momentum m (mass of object) is always same so we can say </mo></mrow><mimathvariant="normal">Δ</mi><mi>x</mi><mo>.</mo><mi>m</mi><mo>.</mo><mimathvariant="normal">Δ</mi><mi>v</mi><mo>≥</mo><mrowdata−mjx−texclass="ORD"><mfrac><mi>h</mi><mrowdata−mjx−texclass="ORD"><mn>4</mn><mi>π</mi></mrow></mfrac></mrow></math></mjx−assistive−mml></mjx−container></mjx−assistive−mml></mjx−container></mo></mrow><mi mathvariant="normal">Δ</mi><mi>x</mi><mo>.</mo><mi>m</mi><mo>.</mo><mi mathvariant="normal">Δ</mi><mi>v</mi><mo>≥</mo><mrow data-mjx-texclass="ORD"><mfrac><mi>h</mi><mrow data-mjx-texclass="ORD"><mn>4</mn><mi>π</mi></mrow></mfrac></mrow></math></mjx-assistive-mml></mjx-container></mjx-assistive-mml></mjx-container> Mass of the particle (m) = 25 g = 0.025 kg

Position of the particle (Δx) = 10-5 m

Δx.Δp = h4π

Δx.m.Δv = h4π

Δv = h4×Δx×m×π

Δv = 6.6×10−344×10−5×0.025×3.14

Δv = 2.1 × 10-28

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