Final answer:
If the Sun were replaced with a one-solar-mass black hole, Earth's orbit would remain the same, but the planet would become cold and dark, leading to the potential extinction of life.
Step-by-step explanation:
If the Sun were replaced with a one-solar-mass black hole, there would be no change to the period of Earth's revolution around it. This is because the gravitational pull on the Earth would remain the same; only the mass and the corresponding gravitational force are relevant for the orbit, according to Kepler's Laws and Newton's Universal Law of Gravitation. The black hole would have the same mass as the Sun and hence exert the same gravitational force on Earth assuming its distance remains unchanged. Since the Earth's orbit is primarily determined by the mass of the Sun and not its size, the Earth would continue to orbit the one-solar-mass black hole at the same distance and with the same period as it orbits the current Sun.
The key difference, however, would relate to the lack of light and heat since black holes do not emit energy like a star. The immediate consequence would be that our planet would become extremely cold and dark, leading to the extinction of life as we know it.