Match List-I (Experiment performed) with List-II (Phenomena discovered/associated) and select the correct option from the options given below the lists.

List-I:                                                                  List-II:
(a) Davisson and Germer experiment                    (i) Wave nature of electrons
(b) Millikan's oil drop experiment                         (ii) Charge of an electron
(c) Rutherford experiment                                   (iii) Quantisation of energy levels
(d) Franck-Hertz experiment                               (iv) Existence of the nucleus

Let us solve this matching question step by step by recalling the key discoveries associated with each experiment.

First, consider experiment (a) Davisson and Germer experiment. In this experiment, electrons were scattered by a nickel crystal, and an interference pattern was observed. This interference pattern is characteristic of waves, demonstrating that electrons exhibit wave-like behavior. Therefore, Davisson and Germer experiment is associated with the wave nature of electrons, which corresponds to List-II option (i).

Next, experiment (b) Millikan's oil drop experiment. Here, tiny oil droplets were suspended in an electric field, and their charges were measured. The charges were always found to be integer multiples of a fundamental value, which is the charge of a single electron. Thus, Millikan's experiment determined the charge of an electron, matching List-II option (ii).

Now, experiment (c) Rutherford experiment. This involved firing alpha particles at a thin gold foil. Most particles passed through, but some were deflected at large angles, indicating a dense, positively charged core in the atom. This led to the discovery of the atomic nucleus. Hence, Rutherford experiment corresponds to List-II option (iv) Existence of the nucleus.

Finally, experiment (d) Franck-Hertz experiment. Electrons were accelerated through mercury vapor, and collisions showed discrete energy losses. This proved that atoms absorb energy in specific quantized amounts, confirming quantized energy levels. Therefore, Franck-Hertz experiment matches List-II option (iii) Quantisation of energy levels.

Summarizing the matches:

• (a) Davisson and Germer experiment → (i) Wave nature of electrons
• (b) Millikan's oil drop experiment → (ii) Charge of an electron
• (c) Rutherford experiment → (iv) Existence of the nucleus
• (d) Franck-Hertz experiment → (iii) Quantisation of energy levels

Comparing with the given options:

• Option A: (a)-(iii), (b)-(iv), (c)-(i), (d)-(ii) → Incorrect
• Option B: (a)-(i), (b)-(ii), (c)-(iv), (d)-(iii) → Correct
• Option C: (a)-(iv), (b)-(iii), (c)-(ii), (d)-(i) → Incorrect
• Option D: (a)-(i), (b)-(ii), (c)-(iii), (d)-(iv) → Incorrect

Hence, the correct answer is Option B.