The minimum uncertainty in the velocity of a ping-pong ball is to be determined and a comment is to be made on the magnitude of the uncertainty in the speed. Concept introduction: According to the Heisenberg uncertainty principle, the product of the uncertainty in the position and the momentum of a particle cannot be less than h 4 π . It is expressed as follows: Δ x ⋅ Δ p ≥ h 4 π Here, Δ x is the uncertainty in position, Δ p is the uncertainty in momentum, and h is Planck’s constant ( 6.63 × 10 − 34 J ⋅ s ) . As momentum is the product of mass and velocity, the equation of the Heisenberg uncertainty principle can also be written as follows: Δ x ⋅ m Δ u ≥ h 4 π Here, Δ x is the uncertainty in the position of a particle, m is the mass of the particle, Δ u is the uncertainty in velocity, and h is Planck’s constant ( 6.63 × 10 − 34 J ⋅ s ) . Conversion factor for nm to meter is 1.0 nm 1.0 × 10 − 9 m . Conversion factor for gram to kilogram is: 1000 g 1.0 kg .

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Answer 1

Question

Chapter 6, Problem 53QP

Interpretation Introduction

Interpretation:

The minimum uncertainty in the velocity of a ping-pong ball is to be determined and a comment is to be made on the magnitude of the uncertainty in the speed.

Concept introduction:

According to the Heisenberg uncertainty principle, the product of the uncertainty in the position and the momentum of a particle cannot be less than $h4π$ . It is expressed as follows:

$Δx⋅Δp≥h4π$

Here, $Δx$ is the uncertainty in position, $Δp$ is the uncertainty in momentum, and $h$ is Planck’s constant $(6.63×10−34 J⋅s)$ .

As momentum is the product of mass and velocity, the equation of the Heisenberg uncertainty principle can also be written as follows:

$Δx⋅mΔu≥h4π$

Here, $Δx$ is the uncertainty in the position of a particle, $m$ is the mass of the particle, $Δu$ is the uncertainty in velocity, and $h$ is Planck’s constant $(6.63×10−34 J⋅s)$ .

$Conversion factor for nm to meter is1.0 nm1.0×10−9 m$ .

$Conversion factor for gram to kilogram is:1000 g1.0 kg$ .

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Answer 2

Question

Chapter 6, Problem 53QP

Interpretation Introduction

Interpretation:

The minimum uncertainty in the velocity of a ping-pong ball is to be determined and a comment is to be made on the magnitude of the uncertainty in the speed.

Concept introduction:

According to the Heisenberg uncertainty principle, the product of the uncertainty in the position and the momentum of a particle cannot be less than $h4π$ . It is expressed as follows:

$Δx⋅Δp≥h4π$

Here, $Δx$ is the uncertainty in position, $Δp$ is the uncertainty in momentum, and $h$ is Planck’s constant $(6.63×10−34 J⋅s)$ .

As momentum is the product of mass and velocity, the equation of the Heisenberg uncertainty principle can also be written as follows:

$Δx⋅mΔu≥h4π$

Here, $Δx$ is the uncertainty in the position of a particle, $m$ is the mass of the particle, $Δu$ is the uncertainty in velocity, and $h$ is Planck’s constant $(6.63×10−34 J⋅s)$ .

$Conversion factor for nm to meter is1.0 nm1.0×10−9 m$ .

$Conversion factor for gram to kilogram is:1000 g1.0 kg$ .

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Answer 3

Question

Chapter 6, Problem 53QP

Interpretation Introduction

Interpretation:

The minimum uncertainty in the velocity of a ping-pong ball is to be determined and a comment is to be made on the magnitude of the uncertainty in the speed.

Concept introduction:

According to the Heisenberg uncertainty principle, the product of the uncertainty in the position and the momentum of a particle cannot be less than $h4π$ . It is expressed as follows:

$Δx⋅Δp≥h4π$

Here, $Δx$ is the uncertainty in position, $Δp$ is the uncertainty in momentum, and $h$ is Planck’s constant $(6.63×10−34 J⋅s)$ .

As momentum is the product of mass and velocity, the equation of the Heisenberg uncertainty principle can also be written as follows:

$Δx⋅mΔu≥h4π$

Here, $Δx$ is the uncertainty in the position of a particle, $m$ is the mass of the particle, $Δu$ is the uncertainty in velocity, and $h$ is Planck’s constant $(6.63×10−34 J⋅s)$ .

$Conversion factor for nm to meter is1.0 nm1.0×10−9 m$ .

$Conversion factor for gram to kilogram is:1000 g1.0 kg$ .

Expert Solution & Answer

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Answer 4

Question

Chapter 6, Problem 53QP

Interpretation Introduction

Interpretation:

The minimum uncertainty in the velocity of a ping-pong ball is to be determined and a comment is to be made on the magnitude of the uncertainty in the speed.

Concept introduction:

According to the Heisenberg uncertainty principle, the product of the uncertainty in the position and the momentum of a particle cannot be less than $h4π$ . It is expressed as follows:

$Δx⋅Δp≥h4π$

Here, $Δx$ is the uncertainty in position, $Δp$ is the uncertainty in momentum, and $h$ is Planck’s constant $(6.63×10−34 J⋅s)$ .

As momentum is the product of mass and velocity, the equation of the Heisenberg uncertainty principle can also be written as follows:

$Δx⋅mΔu≥h4π$

Here, $Δx$ is the uncertainty in the position of a particle, $m$ is the mass of the particle, $Δu$ is the uncertainty in velocity, and $h$ is Planck’s constant $(6.63×10−34 J⋅s)$ .

$Conversion factor for nm to meter is1.0 nm1.0×10−9 m$ .

$Conversion factor for gram to kilogram is:1000 g1.0 kg$ .

Expert Solution & Answer

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Answer 5

Chapter 6, Problem 53QP

Interpretation Introduction

Interpretation:

The minimum uncertainty in the velocity of a ping-pong ball is to be determined and a comment is to be made on the magnitude of the uncertainty in the speed.

Concept introduction:

According to the Heisenberg uncertainty principle, the product of the uncertainty in the position and the momentum of a particle cannot be less than $h4π$ . It is expressed as follows:

$Δx⋅Δp≥h4π$

Here, $Δx$ is the uncertainty in position, $Δp$ is the uncertainty in momentum, and $h$ is Planck’s constant $(6.63×10−34 J⋅s)$ .

As momentum is the product of mass and velocity, the equation of the Heisenberg uncertainty principle can also be written as follows:

$Δx⋅mΔu≥h4π$

Here, $Δx$ is the uncertainty in the position of a particle, $m$ is the mass of the particle, $Δu$ is the uncertainty in velocity, and $h$ is Planck’s constant $(6.63×10−34 J⋅s)$ .

$Conversion factor for nm to meter is1.0 nm1.0×10−9 m$ .

$Conversion factor for gram to kilogram is:1000 g1.0 kg$ .

Answer 6

Chapter 6, Problem 53QP

Interpretation Introduction

Interpretation:

The minimum uncertainty in the velocity of a ping-pong ball is to be determined and a comment is to be made on the magnitude of the uncertainty in the speed.

Concept introduction:

According to the Heisenberg uncertainty principle, the product of the uncertainty in the position and the momentum of a particle cannot be less than $h4π$ . It is expressed as follows:

$Δx⋅Δp≥h4π$

Here, $Δx$ is the uncertainty in position, $Δp$ is the uncertainty in momentum, and $h$ is Planck’s constant $(6.63×10−34 J⋅s)$ .

As momentum is the product of mass and velocity, the equation of the Heisenberg uncertainty principle can also be written as follows:

$Δx⋅mΔu≥h4π$

Here, $Δx$ is the uncertainty in the position of a particle, $m$ is the mass of the particle, $Δu$ is the uncertainty in velocity, and $h$ is Planck’s constant $(6.63×10−34 J⋅s)$ .

$Conversion factor for nm to meter is1.0 nm1.0×10−9 m$ .

$Conversion factor for gram to kilogram is:1000 g1.0 kg$ .

Answer 7

Chapter 6, Problem 53QP

Interpretation Introduction

Interpretation:

The minimum uncertainty in the velocity of a ping-pong ball is to be determined and a comment is to be made on the magnitude of the uncertainty in the speed.

Concept introduction:

According to the Heisenberg uncertainty principle, the product of the uncertainty in the position and the momentum of a particle cannot be less than $h4π$ . It is expressed as follows:

$Δx⋅Δp≥h4π$

Here, $Δx$ is the uncertainty in position, $Δp$ is the uncertainty in momentum, and $h$ is Planck’s constant $(6.63×10−34 J⋅s)$ .

As momentum is the product of mass and velocity, the equation of the Heisenberg uncertainty principle can also be written as follows:

$Δx⋅mΔu≥h4π$

Here, $Δx$ is the uncertainty in the position of a particle, $m$ is the mass of the particle, $Δu$ is the uncertainty in velocity, and $h$ is Planck’s constant $(6.63×10−34 J⋅s)$ .

$Conversion factor for nm to meter is1.0 nm1.0×10−9 m$ .

$Conversion factor for gram to kilogram is:1000 g1.0 kg$ .

Answer 8

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Answer 9

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Answer 10

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Answer 11

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Solution Summary: The author explains that the minimum uncertainty in the velocity of a ping-pong ball is to be determined. The equation of the Heisenberg uncertainty principle can also be written as follows:

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