Q.(a) State Faraday's II law of electrolysis. How is it verified experimentally ? OR

(a) Faraday's second law of electrolysis says that for the same charge passed, the mass liberated at an electrode is proportional to the substance's chemical equivalent weight; this is verified experimentally using voltameters in series. (b) Raman scattering produces frequency-shifted spectral lines (Stokes and anti-Stokes) on either side of the unshifted Rayleigh line, due to inelastic scattering of light by molecules. Both alternatives are answered in full below.

(a) Faraday's second law of electrolysis and its experimental verification

Statement: When the same quantity of electricity (charge) is passed through several different electrolytes (voltameters) connected in series, the masses of the substances liberated at their respective electrodes are directly proportional to their chemical equivalent weights (equivalent weight $E$ = atomic/molecular weight $\div$ valency). That is,

$m \propto E \quad\Rightarrow\quad \dfrac{m_1}{E_1} = \dfrac{m_2}{E_2} = \dfrac{m_3}{E_3} = \dots = \text{constant}$

Experimental verification: A copper voltameter and a silver voltameter are connected in series with a battery, rheostat, ammeter, and key, so that exactly the same current $I$ flows through both for the same time $t$ — i.e. the same charge $Q = It$ passes through each. The cathode of each voltameter is cleaned, dried, and weighed before the experiment, and again after passing the current for a measured time. The mass deposited on the copper cathode ($m_{Cu}$) and on the silver cathode ($m_{Ag}$) are found from the before/after weights.

The chemical equivalents of copper and silver are known: $E_{Cu} = 63.5/2 = 31.75$ (copper is divalent) and $E_{Ag} = 108/1 = 108$ (silver is monovalent). Since the same charge passed through both voltameters, Faraday's second law predicts

$\dfrac{m_{Cu}}{E_{Cu}} = \dfrac{m_{Ag}}{E_{Ag}}$

Experimentally, the measured masses are found to satisfy this ratio to good accuracy, confirming the law.

(b) Raman scattering of light

When a beam of monochromatic light of frequency $\nu_0$ passes through a transparent medium (a liquid, gas, or transparent solid) and the scattered light is examined at right angles with a spectrometer, most of the scattered light is found to have the same frequency $\nu_0$ as the incident light — this unshifted, strong line is called the Rayleigh line, arising from elastic scattering in which the photon exchanges no net energy with the molecule.

However, C.V. Raman (1928) discovered that in addition to the Rayleigh line, the scattered light contains a number of much weaker lines at frequencies $\nu_0 -\nu_m$ and $\nu_0 +\nu_m$, symmetrically placed on either side of the Rayleigh line, where $\nu_m$ is a frequency characteristic of the vibrational (or rotational) energy levels of the scattering molecule and is independent of $\nu_0$. This phenomenon is called the Raman effect.

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