What is the relationship between Speciation and Adaptive Radiation?

Hint: Adaptation has three different meanings in biology. To begin with, it is the dynamic evolutionary process that adapts organisms to their surroundings and improves their evolutionary fitness. Second, it is the situation in which the population finds itself during that process. Third, it is a phenotypic characteristic or adaptive trait that has developed via natural selection and has a functional purpose in each particular organism.

Complete step by step solution:
Many speciation-with-gene-flow models include ecological adaptability as a key component. Divergent natural selection exerted by various habitats or settings, in particular, can act as a significant “extrinsic” barrier to gene flow and speciation. A species is a collection of creatures that share similar traits and may interbreed to produce viable offspring. Speciation is the evolutionary process by which new and different species emerge. Genetic alteration is how organisms evolve. The new species are reproductively separated from the old species, which means they can't mate with one other. The creation of new species from existing populations is known as speciation.
The adaptive radiation process explains this variety. A burst of evolution known as adaptive radiation produces numerous new species from a single parent species. It's beneficial to conceive about deserted "islands" of habitat here, much as it was when we examined species richness, albeit the islands just need to be unoccupied by the species in issue. A population of a particular species, which we'll call species 1, enters a new ecosystem and establishes itself in a niche, or function, within it. It adjusts to its new habitat in this way, becoming distinct from the parent species.
If a new population of the parent species, 2, enters the region, it will attempt to fill the same niche as 1. The niche rule, on the other hand, asserts that in any given habitat, only one species from a group of closely related species may occupy the same niche. As a result of the competition between species 1 and 2, both groups are under pressure to adapt to different niches, further separating them from one other and the parent species. Several new species may emerge from a single parent species in a very short amount of time, as this occurs frequently in a particular environment.

Note:
Adaptive radiation is the fast development of many species from a single parent species. It leads to the emergence of new species. When there is an ecological opportunity or the availability of a new adaptive zone to explore, adaptive radiation occurs. E.g. Darwin’s finches in Galapagos island.