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Chapter 3, Problem 3.146QP

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CHEMISTRY: ATOMS FIRST VOL 1 W/CON...

14th Edition
Burdge
ISBN: 9781259327933

Solutions

Chapter
Section
FindFindarrow_forward

CHEMISTRY: ATOMS FIRST VOL 1 W/CON...

14th Edition
Burdge
ISBN: 9781259327933

(a)

Interpretation Introduction

Interpretation:

The minimum uncertainty in the position for an electron in the ground state of the hydrogen atom which moves at an average speed of 5 × 106 m/s and the speed is known to an uncertainty of 20 percent and the uncertainty in the baseball’s position in which 0.15-kg baseball thrown at 99 mph having a momentum of 6.7 kgm/s and the uncertainty in measuring the momentum is 1.0 × 107 should be calculated.

Concept Introduction:

The Heisenberg uncertainty principle says that it is impossible to know simultaneously both the momentum (p) and the position (x) of a particle with certainty.

Mathematically, ΔxΔp  h

For a particle having the mass m, ΔxmΔu   h

where Δx and Δu are uncentainty in measuring the position and velocity of the particle respectively; h is Planck’s constant (6.63 × 1034 Js).

To find: Calculate the minimum uncertainty in the position for an electron in the ground state of the hydrogen atom which moves at an average speed of 5 × 106 m/s and the speed is known to an uncertainty of 20 percent

(b)

Interpretation Introduction

Interpretation:

The minimum uncertainty in the position for an electron in the ground state of the hydrogen atom which moves at an average speed of 5 × 106 m/s and the speed is known to an uncertainty of 20 percent and the uncertainty in the baseball’s position in which 0.15-kg baseball thrown at 99 mph having a momentum of 6.7 kgm/s and the uncertainty in measuring the momentum is 1.0 × 107 should be calculated.

Concept Introduction:

The Heisenberg uncertainty principle says that it is impossible to know simultaneously both the momentum (p) and the position (x) of a particle with certainty.

Mathematically, ΔxΔp  h

For a particle having the mass m, ΔxmΔu   h

where Δx and Δu are uncentainty in measuring the position and velocity of the particle respectively; h is Planck’s constant (6.63 × 1034 Js).

To find: The uncertainty in the baseball’s position in which 0.15-kg baseball thrown at 99 mph having a momentum of 6.7 kgm/s and  the uncertainty in measuring the momentum is 1.0 × 107

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