Cosmologists have speculated that black holes the size of a proton could have formed during the early days of the Big Bang when the universe began. If we take the diameter of a proton to be 1.0 * 10^-15 m, what would be the mass of a mini black hole?

Video transcript

Welcome back everybody. We are looking at many black holes here now. It is told that for a given many black hole, it about has the same diameter as the nucleus of a hydrogen atom. We're told that the radius of a hydrogen nucleus is given by one er mai which is approximately equal to one times 10 to the negative 15th eaters. And we are asked to find what the mass of a mini black hole would be. Well, the radius of a black hole relates to its mass by this equation here, that the radius is equal to two times Newton's gravitational constant times the mass of the black hole, all divided by the speed of light squared, rearranging some firms here, we actually get that the mass of the black hole, which is our desired value is the radius times the speed of light squared. All divided by two times. Newton's gravitational constant. We have all these values. So let's just go ahead and plug in some numbers here. The mass is one times 10 to the negative 15th meters. The radius times three times 10 to the eighth, which is the speed of light squared divided by two times. Newton's gravitational constant of 6.67 times 10 to the negative 11. Which when you plug into your calculator, you get that The mass of a mini black hole is approximately 6. times 10 to the 11th kilograms. So a mini black hole is still pretty heavy and that gives us a final answer of D. Thank you all so much for watching. Hope this video helped. We will see you all in the next one.