Chapter 7, Problem 7.81P

(a)

Interpretation Introduction

Interpretation:

The highest frequency and minimum wavelength of radiation emitted when the electron makes a transition from $n=3$ is to be determined.

Concept introduction:

Electromagnetic waves are radiations that are formed by oscillating electric and magnetic fields. The electric and magnetic field components of an electromagnetic wave are perpendicular to each other.

The difference between the energies of two energy levels is the amount of energy in a photon emitted or absorbed when an electron makes a transition. The energy of a photon emitted or absorbed by an electron is,

$\Delta E=h\nu$ (1)

Here,

$\Delta E$ is the energy.

$h$ is the Plank’s constant.

$\nu$ is the frequency

(b)

Interpretation Introduction

Interpretation:

The ionization energy of the atom in its ground state in $\text{kJ/mol}$ is to be determined.

Concept introduction:

Ionization energy is defined as the amount of energy required to remove an electron from an isolated gaseous atom. The energy required to remove an electron from an atom depends on the position of the electron in the atom. The closer the electron is to the nucleus in the atom, the harder it is to pull it out of the atom. As the distance of an electron from the nucleus increases, the magnitude of the forces of attraction between the electron and the nucleus decreases. Thus it becomes easier to remove it from the atom.

(c)

Interpretation Introduction

Interpretation:

The shortest wavelength of radiation that could be absorbed by the electron in the $n=4$ level without causing ionization is to be determined.

Concept introduction:

Electromagnetic waves are radiations that are formed by oscillating electric and magnetic fields. The electric and magnetic field components of an electromagnetic wave are perpendicular to each other.

The difference between the energies of two energy levels is the amount of energy in a photon emitted or absorbed when an electron makes a transition. The energy of a photon emitted or absorbed by an electron is,

$\Delta E=h\nu$ (1)

Here,

$\Delta E$ is the energy.

$h$ is the Plank’s constant.

$\nu$ is the frequency

The equation to relate the frequency and wavelength of radiation is as follows:

$\nu =\frac{c}{\lambda }$

The above relation can be modified as follows:

$\Delta E=\frac{hc}{\lambda }$ (4)