Tuesday, February 15, 2011

The Density Of A Black Hole

A while ago I had a realization, when reading the Twitter feed of someone who I follow on Twitter. He said something about a black hole must have a volume, because there is a maximum amount of enthalpy that can be held in an area. I'm not sure if this is true or not, I might look into at some time when I'm typing this up because I have a few things I'm going to need to search.. but I decided to try to calculate the density of a black hole.

I feel a bit nerdy at the moment for this, but I'm curious. I'm making a handful of assumptions, such as a black hole has maximum density (minimal distance between atoms), the area that I will be theoretically sampling will consist of only H atoms (the most common atom to find, and I'm assuming due to the density atoms are prone to breaking down into the simplest atom it can). The area that will be sampled will be 1m squared. Hydrogen is diatomic, it usually exists in groupings of two atoms. I will be ignoring this.

So density is calculated by dividing mass by volume. I already know the volume is 1m squared. I need to find the mass. This will be a bit trickier.

by finding the diameter of a hydrogen atom, I can find how many can fit in a 1x1x1m area. After looking at a few sources, such as a question on a forum, Wikipedia article, and a Yahoo question. One note that someone made in the first link, that when looking at an individual atom (especially hydrogen I suppose) the wave properties of it become very apparent rather than the diameter. Never less, I came to the conclusion a hydrogen atom will be approximately 1.6x10^-15m or 0.000000000000016m. I'm not sure how accurate this is, but it is an easy number to work with.

This means a 1m length, of only one dimension, will hold... lets see. 1/1.6^-15 will equal about 625000000000000 or 6.25x10^13. Considering signifigant figures, it should be 6.3x10^13, but I enjoy it the way it is. 6.25x10^13 cubed will equal 2.453125x10^41 hydrogen atoms. I'll round this to 2.45x10^41.

Now that I have the number of hydrogen atoms in the given area, I will have to find the mass. 1 mole of hydrogen will equal 1g, or 0.001kg. Physics works better with kg, or it's what I'm use to at least. Physics 11 class got me in the habit. 1 mole equals 6.02x10^24 atoms. I need to find out how many moles are in 2.45x10^41 atoms. I think I'll grab my graphing calculator for this.

Some number crunching later; 4.069767442x10^16 moles of hydrogen atoms in a 1m cubed area. This will weigh (going to a rounded number) 4.07x10^41 grams or 4.07x10^39 kg. Check my numbers for me? I think they're right so far.

To finish this up, the mass we have found will be divided by the volume. The volume being 1, there doesn't need to be much math. According to my quick calculations and forty minutes of talking to my friends while a throw numbers together has produced my decision that a black hole must have a density, or at least could have a density of:

4.07x10^39 kg per cubic meter. That wasn't all that exciting at all, but I've had the idea to do this for a few months. The idea was written down in my idea book, and it's been one of the few ideas that I have actually perused in it. Next up may be my particle vibration theory.


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