Ch.7 - Quantum MechanicsWorksheetSee all chapters
All Chapters
Ch.1 - Intro to General Chemistry
Ch.2 - Atoms & Elements
Ch.3 - Chemical Reactions
BONUS: Lab Techniques and Procedures
BONUS: Mathematical Operations and Functions
Ch.4 - Chemical Quantities & Aqueous Reactions
Ch.5 - Gases
Ch.6 - Thermochemistry
Ch.7 - Quantum Mechanics
Ch.8 - Periodic Properties of the Elements
Ch.9 - Bonding & Molecular Structure
Ch.10 - Molecular Shapes & Valence Bond Theory
Ch.11 - Liquids, Solids & Intermolecular Forces
Ch.12 - Solutions
Ch.13 - Chemical Kinetics
Ch.14 - Chemical Equilibrium
Ch.15 - Acid and Base Equilibrium
Ch.16 - Aqueous Equilibrium
Ch. 17 - Chemical Thermodynamics
Ch.18 - Electrochemistry
Ch.19 - Nuclear Chemistry
Ch.20 - Organic Chemistry
Ch.22 - Chemistry of the Nonmetals
Ch.23 - Transition Metals and Coordination Compounds

Solution: A student is examining a bacterium under the microscope. The E. coli bacterial cell has a mass of = 0.500 (where a femtogram,fg , is 10-15 g) and is swimming at a velocity of v = 9.00 um/s, with an un

Solution: A student is examining a bacterium under the microscope. The E. coli bacterial cell has a mass of = 0.500 (where a femtogram,fg , is 10-15 g) and is swimming at a velocity of v = 9.00 um/s, with an un

Problem

A student is examining a bacterium under the microscope. The E. coli bacterial cell has a mass of = 0.500 (where a femtogram,fg , is 10-15 g) and is swimming at a velocity of v = 9.00 um/s, with an uncertainty in the velocity of 8.00 %. E. coli bacterial cells are around 1 um (10-6m ) in length. The student is supposed to observe the bacterium and make a drawing. However, the student, having just learned about the Heisenberg uncertainty principle in physics class, complains that she cannot make the drawing. She claims that the uncertainty of the bacterium's position is greater than the microscope's viewing field, and the bacterium is thus impossible to locate.

What is the uncertainty of the position of the bacterium? Express your answer numerically in meters.

Solution

$
 Δx \times Δp \geq \frac{h}{\pi4} \qquad h=6.626 x10^{-34} Js\ or\ kgm^2/s \\
 Δx\times mΔv \geq \frac{h}{\pi4} \quad Δx = uncertainty \ in \ position $

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