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BITSAT 2018
Exam
BITSAT
Year
2018
Subject
Chemistry
Chapter
Structure of Atom

BITSAT 2018 · Chemistry · Structure of Atom

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

In an atom, an electron is moving with a speed of 600m/s600m / s with an accuracy of 0.0050. 005 %. Certainty with which the position of the electron can be located is (h = 6. 6 \times {10}^{- 34}kgm^{2}s^{- 1},massofelectron,, mass of electron,{m}_{e} = 9. 1 \times {10}^{- 31}kg))

Options

  1. A1.52×10−4m1. 52 \times {10}^{- 4}m
  2. B5.10×10−3m5. 10 \times {10}^{- 3}m
  3. C1.92×10−3m1. 92 \times {10}^{- 3}m
  4. D3.84×10−3m3. 84 \times {10}^{- 3}m

Correct answer

C. 1.92×10−3m1. 92 \times {10}^{- 3}m

Step-by-step solution

Given that velocity of electron, v=600m/sv = 600m / s

Accuracy of velocity =0.005= 0.005%

According to Heisenberg's uncertainty principle

\left(\Delta x\right) . \left(m \Delta v\right) = \dfrac{h}{4\pi}</p><p></p><p>∆ v = 0 . 005 %~or&600ms^{- 1}</p><p></p><p>= \dfrac{600 \times 0 . 005}{100} = 0 . 03</p><p></p><p>∆ x \times 9 . 1 \times {10}^{- 31} \times 0 . 03 = \dfrac{6 . 6 \times {10}^{- 34}}{4 \times 3 . 14}</p><p>Hence, </p><p>Hence,~∆ x = \dfrac{6 . 6 \times {10}^{- 34}}{4 \times 3 . 14 \times 0 . 03 \times 9 . 1 \times {10}^{- 31}}</p><p></p><p>= 1 . 92 \times {10}^{- 3}m$

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