Tamil Nadu Board of Secondary EducationHSC Science Class 11

Calculate the uncertainty in position of an electron, if Δv = 0.1% and υ = 2.2 × 106 ms-1 - Chemistry

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Numerical

Calculate the uncertainty in position of an electron, if Δv = 0.1% and υ = 2.2 × 106 ms-1

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Solution

Mass of an electron = m = 9.1 × 10-31 kg.

∆v = Uncertainty in velocity = `0.1/100` × 2.2 × 103 ms-1

∆υ = 0.22 × 104 = 2.2 × 10ms-1

∆x . ∆υ . m = `"h"/(4π)`

∆x = `"h"/(∆"υ" . "m". 4π)`

= `(6.626 xx 10^-34)/(2.2 xx 10^3 xx 9.1 xx 10^-31 xx 4 xx 3.14)`

= `(6.626 xx 10^-34 xx 10^3 xx 10^31)/(2.2 xx 9.1 xx 4 xx 3.14)`

= `(6.626 xx 10^-6)/(251.45)`

= 0.02635 × 10-6

∆x = 2.635 × 10-8
Uncertainty in position = 2.635 × 10-8

Concept: Filling of Orbitals
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Chapter 2: Quantum Mechanical Model of Atom - Evaluation [Page 64]

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Tamil Nadu Board Samacheer Kalvi Class 11th Chemistry Volume 1 and 2 Answers Guide
Chapter 2 Quantum Mechanical Model of Atom
Evaluation | Q II. 9. | Page 64
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