Final answer:
The Earth's orbit around a black hole with the same mass as the Sun would remain the same, and hence there would be no change in the Earth's orbital period. However, the absence of sunlight would cause the Earth's environment to change drastically, eventually leading to a frozen planet devoid of life.
Step-by-step explanation:
If the Sun suddenly collapsed into a black hole without any other catastrophic effects, the Earth's orbit would remain largely unaffected. The gravitational pull of a black hole with the same mass as the Sun would be identical to the Sun's current gravitational pull at the distance of Earth's orbit. Hence, the period of Earth's revolution, or orbital period, around the black hole would not differ from its current yearly cycle. The significant change, though, would be the absence of sunlight, leading to extreme changes in the Earth's environment. Kepler's third law tells us that the orbital period of a planet is related to the mass of the star it orbits and the size of its orbit; since neither the mass of the new black hole (formerly the Sun) nor the size of Earth's orbit would change, neither would the Earth's orbital period.
However, from a broader perspective, this transformation into a black hole would have significant implications for the future of the solar system and any potential for life on Earth. The loss of sunlight would result in a rapid cooling of the Earth's surface, leading to a frozen planet, and eventually, all life as we know it would perish due to the absence of energy from the Sun.