Chapter 4, Problem 59AP

(a)

Interpretation Introduction

Interpretation:de-Broglie wavelength of baseball is to be determined.

Concept introduction:The expression to calculate de-Broglie wavelength of moving particle is as follows:

  $\text{λ}=\frac{h}{mv}$

Where,

• $\text{λ}$ is wavelength.
• $m$ is mass of moving body.
• $v$ is velocity of body.
• $h$ is Plank’s constant.

(b)

Interpretation Introduction

Interpretation: Smallest distance within limits of velocity is to be determined.

Concept introduction: The expression to calculate de-Broglie wavelength of moving particle is as follows:

  $\text{λ}=\frac{h}{mv}$

Where,

• $\text{λ}$ is wavelength.
• $m$ is mass of moving body.
• $v$ is velocity of body.
• $h$ is Plank’s constant.

The expression to calculate uncertainty in position $\left(\Delta x\right)$ of moving body is as follows:

  $\Delta x=\frac{h}{4\text{π}m\Delta v}$

(c)

Interpretation Introduction

Interpretation: The Bohr radius of hydrogen atom should be determined.

Concept introduction: The expression to calculate radius of hydrogen atom is as follows:

  $r=\frac{{\epsilon }_0{h}^2}{\text{π}mZ{e}^2}$

Where,

• $Z$is atomic number.
• $e$ is charge on electron.
• ${\epsilon }_0$ is permittivity of space.
• $h$ is Plank’s constant.
• $m$ is mass of electron.