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JIPMER 2015
Exam
JIPMER
Year
2015
Subject
Chemistry
Chapter
Structure of Atom

JIPMER 2015 · Chemistry · Structure of Atom

In an atom, an electron is moving with a speed of 600 ~m / s with...

In an atom, an electron is moving with a speed of 600 m/s600 \mathrm{~m} / \mathrm{s} with an accuracy of 0.005%0.005 \%. Certainty with which the position of the electron can be located is (Given, h=6.6×10−34 kg m2 s−1h=6.6 \times 10^{-34} \mathrm{~kg} \mathrm{~m}^2 \mathrm{~s}^{-1}, mass of electron em=9.1×10−31 kge_m=9.1 \times 10^{-31} \mathrm{~kg} )

Options

  1. A2.15×10−3 m2.15 \times 10^{-3} \mathrm{~m}
  2. B2.78×10−3 m2.78 \times 10^{-3} \mathrm{~m}
  3. C1.92×10−3 m1.92 \times 10^{-3} \mathrm{~m}
  4. D3.24×10−3 m3.24 \times 10^{-3} \mathrm{~m}

Correct answer

C. 1.92×10−3 m1.92 \times 10^{-3} \mathrm{~m}

Step-by-step solution

Given that velocity of electron, v=600 m/sv=600 \mathrm{~m} / \mathrm{s} Accuracy of velocity =0.005%∴Δv=600×0.005100=0.03=0.005 \% \therefore \quad \Delta v=\frac{600 \times 0.005}{100}=0.03 According to Heisenberg's uncertainty principle Δx.mΔv≥h4π\Delta x . m \Delta v \geq \frac{h}{4 \pi} Or, Δx=6.6×10−344×3.14×9.1×10−31×0.03=1.92×10−3 m\begin{aligned} \Delta x & =\frac{6.6 \times 10^{-34}}{4 \times 3.14 \times 9.1 \times 10^{-31} \times 0.03} \\ & =1.92 \times 10^{-3} \mathrm{~m}\end{aligned}
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