Chapter 3, Problem 7P

(a)

Interpretation Introduction

Interpretation:

The magnitude of the force on the electron at each separation should be calculated.

Concept Introduction:

The formula which is used to calculate the force between proton and electron separated by distance is given by:

  $F_{coulomb}=-\frac{Z{e}^2}{4\pi {\epsilon }_0{r}^2}$

Where, $F_{coulomb}$ = Force

Z = Atomic number.

  $e$ is the charge on electron.

r is the distance between proton and electron.

(b)

Interpretation Introduction

Interpretation:

The change in potential energy between the proton and electron should be calculated.

Concept Introduction:

The energy which is possessed by an object or material due to its composition or position with respect to other objects or materialis said to be potential energy

The formula which is used to calculate the potential energy between electron and proton separated by distance is given by:

  $V(r)=-\frac{q_1{q}_2}{4\pi {\epsilon }_{0}r}$

Where, $V(r)$ = Potential energy

  $q_1$ and $q_2$ = charge on electron and proton.

r is the distance between the proton and electron.

(c)

Interpretation Introduction

Interpretation:

The change in the speed of the electron should be calculated when the electron was initially stationary.

Concept Introduction:

The following formula is used for calculating the change in speed of the electron is:

  $m\upsilon r=\frac{nh}{2\pi }$

Where, m = mass of electron ( $9.1\times {10}^{-31}\text{ kg}$ )

  $\upsilon$ = velocity of the electron

r = radius of the electron ( $0.529\times {10}^{-10}\text{ m}$ )

h = Planck’s constant ( $6.626\times {10}^{-34}{\text{ m}}^2{\text{kgs}}^{-1}$ )

n = principal quantum number

The relation between radius and principal quantum number is:

  $r_o=0.529\times \frac{n^2}{Z}$

Where, $r_o$ = radius

Z = atomic number

n = principal quantum number