WebAssign for Zumdahl/Zumdahl/DeCoste's Chemistry, 10th Edition [Instant Access], Single-Term
WebAssign for Zumdahl/Zumdahl/DeCoste's Chemistry, 10th Edition [Instant Access], Single-Term
10th Edition
ISBN: 9781337909969
Author: Zumdahl; Steven S.
Publisher: Cengage Learning US
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Chapter 7, Problem 75E

Using the Heisenberg uncertainty principle, calculate Δx for each of the following.

a. an electron with Δv = 0.100 m/s

b. a baseball (mass = 145 g) with Δv = 0.100 m/s

How does the answer in part a compare with the size of a hydrogen atom? How does the answer in part b correspond to the size of a baseball?

(a)

Expert Solution
Check Mark
Interpretation Introduction

Interpretation:

The uncertainty in velocity of an electron and a baseball is given. Using these values, the uncertainty in the position is to be calculated. Also, the answers obtained are comparing with the size of atom and the size of the baseball.

Concept introduction:

Heisenberg uncertainty principle states that “simultaneous precise measurement of momentum and position of a particle is not possible at the same time.” The product of uncertainty in position and uncertainty in momentum is always a constant.

To determine: Uncertainty in the position Δx of electron with Δv=0.100m/s .

Answer to Problem 75E

Answer

Uncertainty in position of electron is 5.8×10-4m_ .

Explanation of Solution

Given

Uncertainty in velocity of electron, Δv=0.100m/s

Calculate the uncertainty in the position using the formula,

ΔxΔ(mv)h4πΔxh4πmΔv

Where,

  • Δx is the uncertainty in position.
  • Δv is the uncertainty in velocity.
  • h is Planck’s constant (6.626×1034Js) .
  • m is the mass of electron (9.11×1031kg) .

Substitute the values of h,m and Δv in the above equation.

Δxh4πmΔv6.626×1034Js4×3.14×(9.1×1031kg)×(0.100m/s)5.8×104m

Thus, the uncertainty in the position of electron is 5.8×10-4m_ .

Conclusion

Uncertainty in the position of an electron is 5.8×104m .

(b)

Expert Solution
Check Mark
Interpretation Introduction

Interpretation:

The uncertainty in velocity of an electron and a baseball is given. Using these values, the uncertainty in the position is to be calculated. Also, the answers obtained are comparing with the size of atom and the size of the baseball.

Concept introduction:

Heisenberg uncertainty principle states that “simultaneous precise measurement of momentum and position of a particle is not possible at the same time.” The product of uncertainty in position and uncertainty in momentum is always a constant.

To determine: Uncertainty in position Δx of the baseball with Δv=0.100m/s .

Answer to Problem 75E

Answer

Uncertainty in position of baseball is 3.64×10-33m_ .

Explanation of Solution

Given

Uncertainty in velocity of baseball, Δv=0.100m/s

Mass of baseball, m=145g

The conversion of gram (g) into kilograms (kg) is done as,

1g=11000kg

Hence, the conversion of 145g into kilograms is,

145g=145×11000kg=0.145kg

Calculate the uncertainty in the position using the formula,

ΔxΔ(mv)h4πΔxh4πmΔv

Where,

  • Δx is the uncertainty in position.
  • Δv is the uncertainty in velocity.
  • h is Planck’s constant (6.626×1034Js) .
  • m is the mass of baseball.

Substitute the values of h,m and Δv in the above equation.

Δxh4πmΔv6.626×1034Js4×3.14×(0.145kg)×(0.100m/s)3.64×1033m

Thus, the uncertainty in the position of baseball is 3.64×10-33m_ .

Conclusion

Uncertainty in position of a baseball is 3.64×1033m .

(c)

Expert Solution
Check Mark
Interpretation Introduction

Interpretation:

The uncertainty in velocity of an electron and a baseball is given. Using these values, the uncertainty in the position is to be calculated. Also, the answers obtained are comparing with the size of atom and the size of the baseball.

Concept introduction:

Heisenberg uncertainty principle states that “simultaneous precise measurement of momentum and position of a particle is not possible at the same time.” The product of uncertainty in position and uncertainty in momentum is always a constant.

To determine: Compare the answer of part (a) with the size of hydrogen atom.

Answer to Problem 75E

Answer

The uncertainty in part (a) is much larger than size of the hydrogen atom.

Explanation of Solution

Uncertainty in the position of electron is 5.8×104m , whereas the size of hydrogen atom is of the order of 1012m . Therefore, the uncertainty in the position of electron is very large compare to the size of hydrogen atom.

Conclusion

The uncertainty in the position of electron is much larger as compare to size of hydrogen atom.

(d)

Expert Solution
Check Mark
Interpretation Introduction

Interpretation:

The uncertainty in velocity of an electron and a baseball is given. Using these values, the uncertainty in the position is to be calculated. Also, the answers obtained are comparing with the size of atom and the size of the baseball.

Concept introduction:

Heisenberg uncertainty principle states that “simultaneous precise measurement of momentum and position of a particle is not possible at the same time.” The product of uncertainty in position and uncertainty in momentum is always a constant.

To determine: Compare the answer of part (b) with size of baseball.

Answer to Problem 75E

Answer

The uncertainty in part (b) is negligible (insignificant) when compare to the size of baseball.

Explanation of Solution

Uncertainty in the position of baseball is 3.64×1033m , whereas the size of baseball is much larger than this. Therefore, the uncertainty is negligible as compare to the size of baseball.

Conclusion

The uncertainty in part (b) is negligible (insignificant) when compare to size of baseball.

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Chapter 7 Solutions

WebAssign for Zumdahl/Zumdahl/DeCoste's Chemistry, 10th Edition [Instant Access], Single-Term

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