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AIIMS 201826 May
Exam
AIIMS
Year
2018
Date
26 May
Subject
Chemistry
Chapter
Structure of Atom

AIIMS 2018 · 26 May · Chemistry · Structure of Atom

The position of both an electron and helium atom is known within...

The position of both an electron and helium atom is known within 1.0 nm1.0 \mathrm{~nm}. The momentum of the electron is known within 5.0×10−26 kg m s−15.0 \times 10^{-26} \mathrm{~kg} \mathrm{~m} \mathrm{~s}^{-1}. The minimum uncertainty in the measurement of the momentum of the helium atom is

Options

  1. A7.0×10−26 kg m s−17.0 \times 10^{-26} \mathrm{~kg} \mathrm{~m} \mathrm{~s}^{-1}
  2. B5.0×10−26 kg m s−15.0 \times 10^{-26} \mathrm{~kg} \mathrm{~m} \mathrm{~s}^{-1}
  3. C8.0×10−26 kg m s−18.0 \times 10^{-26} \mathrm{~kg} \mathrm{~m} \mathrm{~s}^{-1}
  4. D6.0×10−26 kg m s−16.0 \times 10^{-26} \mathrm{~kg} \mathrm{~m} \mathrm{~s}^{-1}

Correct answer

B. 5.0×10−26 kg m s−15.0 \times 10^{-26} \mathrm{~kg} \mathrm{~m} \mathrm{~s}^{-1}

Step-by-step solution

The Heisenberg uncertainty principle, Δx×Δp≥h4π\Delta x \times \Delta p \geq \frac{h}{4 \pi}, where Δx=\Delta x= Uncertainty in position, Δp=\Delta p= Uncertainty in momentum and h/4π=h / 4 \pi= constant. As Δx\Delta x is same for electron and helium and h/4πh / 4 \pi is a constant, therefore minimum uncertainty in the measurement of the momentum of the helium atom will be same as that of an electron which is 5.0×10−26 kg m s−15.0 \times 10^{-26} \mathrm{~kg} \mathrm{~m} \mathrm{~s}^{-1}.
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