Question

Say I rolled a marble down a funnel so that it essentially spiralled into the center and fell through the funnel hole. How would you calculate the number of revolutions around the funnel this marble made before reaching the center of the funnel? I'm using this similarity to find the amount of revolutions an electron would make before it hit the nucleus of a hydrogen, but I can't for the life of me think of a way to calculate number of revolutions of an object traveling in a spiral towards a center.

Answer 1

The analogy you are making between the marble and the electron, while appears sound in head, is very wrong actually. This is because unlike the marble that can actually spiral down to the center, the electron cant do so. Because the space between the lowest energy level and the nucleus is known as the forbidden region and henec the electron simply can't exist in that region, to begin with. And even if we talk in a simple classical sense and consider your analogy to be correct then still it would depend on a huge no of factors including the rate of dissipation of electromagnetic radiation of the electron, initial energy level, the type of nucleus ( atomic no), etc.

while you can most definitely calculate the no of revolutions for the marble by using its energy and time relations ( you would need these two to begin within your experiment) it is simply agaisnt the rules of physics for the lectron to spiral down into the nucles.

please let me know if i missed something or if i should eleborate something else. Thanks.