Chapter 7, Problem 7.34P

(a)

Interpretation Introduction

Interpretation:

The absorption and emission transitions in the image are to be determined.

Concept introduction:

Atomic spectrum is a series of electromagnetic radiations absorbed or emitted when electrons in an atom undergo transitions between different energy levels.

Absorption spectra - When an atom is subjected to energy in the form of heat or light, the electrons absorb the energy. If an electron in a lower energy level absorbs a photon whose energy is equal to the difference in the energies of the lower energy level and a higher energy level, the electron jumps to the higher energy level. The absorption spectra are characterized by the presence of a series of dark lines separated by colored bands.

Emission spectra – In the emission spectra, an electron in the higher energy level jumps to a lower energy level by releasing energy. The emission spectra are characterized by the presence of a series of fine lines at specific wavelengths separated by black spaces.

(b)

Interpretation Introduction

Interpretation:

The increasing order of energy of emissions is to be determined.

Concept introduction:

Atomic spectrum is a series of electromagnetic radiations absorbed or emitted when electrons in an atom undergo transitions between different energy levels.

Emission spectra – In the emission spectra, an electron in the higher energy level jumps to a lower energy level by releasing energy. The emission spectra are characterized by the presence of a series of fine lines at specific wavelengths separated by black spaces.

The equation to find the difference in the energy between the two levels in hydrogen-like atoms is,

$\Delta E=-2.18\times {10}^{-18}\text{ J}\left(\frac{1}{n_{\text{final}}^2}-\frac{1}{n_{\text{initial}}^2}\right)$        (1)

Here,

$\Delta E$ is the difference in the energy between two levels.

$n_{\text{final}}$ is the lower energy level.

$n_{\text{initial}}$ is the higher energy level.

(c)

Interpretation Introduction

Interpretation:

The increasing order of the wavelengths for absorption transitions is to be determined.

Concept introduction:

Atomic spectrum is a series of electromagnetic radiations absorbed or emitted when electrons in an atom undergo transitions between different energy levels.

Absorption spectra - When an atom is subjected to energy in the form of heat or light, the electrons absorb the energy. If an electron in a lower energy level absorbs a photon whose energy is equal to the difference in the energies of the lower energy level and a higher energy level, the electron jumps to the higher energy level. The absorption spectra are characterized by the presence of a series of dark lines separated by colored bands.

The equation used to predict the position and wavelength of any line in a given series is called the Rydberg’s equation.

Rydberg’s equation is as follows:

$\frac{1}{\lambda }=R\left(\frac{1}{n_1^2}-\frac{1}{n_2^2}\right)$        (2)

Here,

$\lambda$ is the wavelength of the line.

$n_1$ and $n_2$ are positive integers, with ${\text{n}}_2>n_1$.

$R$ is the Rydberg’s constant.

The conversion factor to convert wavelength from $\text{nm}$ to $\text{m}$ is,

$1\text{nm}=1\times {10}^{-9}\text{ m}$