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Model Paper 8 — Chemistry STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceChemistryModel Paper 81 Mark
MCQ
The product of the uncertainties of the exact position and exact momentum (or velocity) of an electron. The product of their uncertainties is always
  • A
    equal to or greater than $h / 3 \pi$
  • ✓
    equal to or greater than $h / 4 \pi$
  • C
    equal to or greater than $h / 2 \pi$
  • D
    equal to or greater than $h / \pi$
✓

Answer

Correct option: B.
equal to or greater than $h / 4 \pi$
(b) equal to or greater than $h / 4 \pi$.
Explanation: The uncertainty principle says that we cannot measure the position ( x ) and the momentum ( p ) of a particle with absolute precision. The more accurately we know one of these values, the less accurately we know the other. Multiplying together the errors in the measurements of these values has to give a number greater than or equal to half of a constant called "h-bar". This is equal to Planck's constant (usually written as h) divided by $2 \pi$.
$
\Delta x \cdot \Delta p \geq \frac{h}{4 \pi}
$

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