Q.(a) Explain the spectral series of hydrogen atom. (Diagram not necessary) OR

(a) The hydrogen spectrum, arising from electron transitions between Bohr energy levels, groups into named series (Lyman, Balmer, Paschen, Brackett, Pfund) according to the final energy level $n_1$, each obeying the Rydberg formula. (b) An AM radio transmitter combines an amplified audio signal with a high-frequency carrier in a modulator, then radiates the amplified AM wave via an antenna. Both alternatives are answered in full below.

(a) Spectral series of the hydrogen atom

In the Bohr model, the electron in a hydrogen atom can exist only in certain discrete, stationary energy levels labelled by the principal quantum number $n = 1, 2, 3, \dots$, with energy $E_n = -13.6\,\text{eV}/n^2$. When the electron makes a transition from a higher level $n_2$ to a lower level $n_1$ ($n_2>n_1$), it emits a photon of energy $h\nu = E_{n_2}-E_{n_1}$, whose wavenumber is given by the Rydberg formula

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

where $R = 1.097\times10^7\,\text{m}^{-1}$ is the Rydberg constant.

For a fixed lower level $n_1$, the transitions from all higher levels $n_2 = n_1+1, n_1+2,\dots$ form a group of spectral lines called a series, converging to a series limit ($1/\lambda_{limit} = R/n_1^2$) as $n_2 \to \infty$. The named series are:

• Lyman series ($n_1=1$, $n_2=2,3,4,\dots$): lies in the ultraviolet region.
• Balmer series ($n_1=2$, $n_2=3,4,5,\dots$): lies in the visible region (the only series visible to the eye).
• Paschen series ($n_1=3$, $n_2=4,5,6,\dots$): lies in the infrared region.
• Brackett series ($n_1=4$, $n_2=5,6,7,\dots$): lies in the infrared region.
• Pfund series ($n_1=5$, $n_2=6,7,8,\dots$): lies in the (far) infrared region.

Each series' lines get progressively closer together and weaker in intensity as $n_2$ increases, converging to the series limit.

(b) AM radio transmitter

An amplitude-modulated (AM) radio transmitter converts a sound signal into a radio wave for broadcasting, through the following blocks in sequence:

1. Microphone: converts the sound (audio) signal into a corresponding weak electrical audio-frequency (AF) signal.
2. Audio amplifier: amplifies this weak AF electrical signal to a level suitable for modulation. …