Match List I (Wavelength range of electromagnetic spectrum) with List II (Method of production of these waves) and select the correct option from the options given below the lists.

List I:                                           List II:
(a) 700 nm to 1 mm                     (i) Vibration of atoms and molecules 
(b) 1 nm to 400 nm                      (ii) Inner shell electrons in atoms moving from one energy level to a lower level
(c) < 10$$^{-3}$$ nm                               (iii) Radioactive decay of the nucleus
(d) 1 mm to 0.1 m                        (iv) Magnetron valve

First, let's recall the electromagnetic spectrum and the typical methods of production for each type of wave. We need to match the wavelength ranges in List I with the production methods in List II.

Starting with (a) from List I: 700 nm to 1 mm. This range corresponds to infrared waves. Infrared waves are primarily produced by the vibrations of atoms and molecules, especially in heated objects. Therefore, (a) matches with (i) from List II.

Next, (b) from List I: 1 nm to 400 nm. This range includes both X-rays and ultraviolet (UV) waves. Specifically, X-rays have wavelengths from about 0.01 nm to 10 nm, while UV waves range from about 10 nm to 400 nm. The production method involving inner shell electrons moving between energy levels is characteristic of X-rays. Since X-rays fall within this range (1 nm to 10 nm), and the method describes X-ray production, (b) matches with (ii) from List II.

Now, (c) from List I: less than $$10^{-3}$$ nm (which is less than 0.001 nm). This extremely short wavelength corresponds to gamma rays. Gamma rays are produced during radioactive decay of atomic nuclei. Therefore, (c) matches with (iii) from List II.

Finally, (d) from List I: 1 mm to 0.1 m. This range falls within microwaves, which are a subset of radio waves. Microwaves are commonly produced using magnetron valves, as seen in devices like microwave ovens. Thus, (d) matches with (iv) from List II.

Summarizing the matches:

• (a) 700 nm to 1 mm → (i) Vibration of atoms and molecules
• (b) 1 nm to 400 nm → (ii) Inner shell electrons in atoms moving from one energy level to a lower level
• (c) < $$10^{-3}$$ nm → (iii) Radioactive decay of the nucleus
• (d) 1 mm to 0.1 m → (iv) Magnetron valve

Comparing with the options:

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

Hence, the correct answer is Option B.