Final answer:
The transition from n=4 to n=2 has the longest wavelength and corresponds to the Balmer series in the visible light spectrum.
Step-by-step explanation:
The transition accompanied by the emission of radiation with the longest wavelength is from n=4 to n=2 (option a). This is known as the Balmer series transition.
In the Balmer series, transitions occur from higher-energy orbits (n > 2) to the second orbit (n = 2) in a hydrogen atom. The wavelengths of the emitted photons for these transitions correspond to visible light in the electromagnetic spectrum.
For example, the transition from n = 4 to n = 2 results in the emission of a photon with a wavelength of 486 nm (green light).