Atomic Structure Question 413

Question: The position of both, an electron and a helium atom is known within 1.0 nm. Further the momentum of the electron is known within $ 5.0\times {10^{-26}}kgm{s^{-1}} $ . The minimum uncertainty in the measurement of the momentum of the helium atom is

Options:

A) $ 50kgm{s^{-1}} $

B) $ 80kgm{s^{-1}} $

C) $ 8.0\times {10^{-26}}kgm{s^{-1}} $

D) $ 5.0\times {10^{-26}}kgm{s^{-1}} $

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Answer:

Correct Answer: D

Solution:

  • By Heisenberg uncertainty Principle $ \Delta x\times \Delta p=\frac{h}{4\pi } $ (which is constant) As $ \Delta x $ for electron and helium atom is same thus momentum of electron and helium will also be same therefore the momentum of helium atom is equal to $ 5\times {10^{-26}}kg.m.{s^{-~1}}. $


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