Final answer:
The correct energy pathway for particles moving inward through an accretion disc toward a black hole is an increase in kinetic energy due to the transformation of potential energy into kinetic energy as they fall deeper into the gravitational well of the black hole.
Step-by-step explanation:
The correct energy pathway for particles gradually moving inward through an accretion disc toward a black hole is increasing kinetic energy.
As particles get closer to the black hole, they fall deeper into the gravitational well, converting their potential energy into kinetic energy. This is due to the conservation of angular momentum, which causes the particles to speed up as they move inward and lose altitude in the gravitational well, much like a figure skater pulling in their arms to spin faster.
According to the principle of energy conservation, despite the turbulent environment of the accretion disc, if we ignore external forces like radiation or magnetic fields, the total energy (potential plus kinetic) of a particle remains constant. However, as the potential energy decreases due to the particle getting closer to the black hole, kinetic energy must increase correspondingly.
The correct choice from the options provided is b. Potential energy is being transformed into kinetic energy. This process explains why particles accelerate to extremely high velocities as they approach a black hole.