Solve Mystery: Properties of Matter Q: Thimble of Water in Ocean

In summary, the probability of picking up at least one of the original molecules from the initial thimble in a thimble of water taken from anywhere in the ocean is 10^23/10^46, which simplifies to 1/10^23. This means that there is a very high likelihood of picking up one of the original molecules from the thimble in the ocean, as there are a huge number of H2O molecules in the ocean compared to the thimble. This can be compared to the probability of picking a specific object from a bag containing many objects, where the number of objects you are looking for is much smaller than the total number of objects in the bag.
  • #1
NZ-Minty
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Q. There are approx 10^23 H2O molecules in a thimble of water adn 10^46 H2O molecules in the ocean. You threw a thimble of water into the ocean and it mixed uniformly. Show that if you dip a thimble of water from anywhere in the ocean that you will probably scoop up at least one of the molecules from thr original thimble.

S. I have no idea how to even attempt answering this Q so any help appreciated.
 
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  • #2
When the molecules from the initial thimble have been mixed uniformly, what is the probability of picking one of those molecules out of the ocean?
 
  • #3
Jgens - thanks for your quick response!

Well 10^46 is 10^23 squared. So would that mean that the ratio is 1:2 so there would be a 50% chance of picking up one of the original molecules ??
 
  • #4
Not quite, n/n^2 is not necessarily equal to 1/2 (in fact it usually isn't). Try another approach for finding the probability.

Hint: It's similar to a problem like if there are n red objects in a bag containing m items, what is the probability of picking a red object from the bag?

Note: I think you might want to brush up on your ratios. If a ratio was 1:2 there would be a 1/3 chance of picking one of the objects.
 
  • #5
Oh dear probabilities aren't something I am good at. :eek:( Still very confused and not understanding this. This is a Q from a intro physics course that is supposed to be helping me to understand physics - I am more confused then ever! :eek:(
 
  • #6
I'm sorry. Here's a concrete example: Suppose I have a bag with 10 objects in it. If there are 4 squares in the bag, what is the probability that I will draw out a square?

Use similar logic to solve your initial problem.
 
  • #7
So the probability for your example would be 4/10 --> 2/5 (or 0.4) Is this correct?

That would make it 10^23/10^46 ...ok need to remember how to put exponents in my calculator - will go and find manual but I think its 1/2 or 0.5 am I on the right track?
 
  • #8
Yes, that's correct.

Well, you can use your calculator. Or you could just use the fact that x^n/x^m = x^(n-m).

Edit: Just realized the second half of you post. 1/2 is definitely not correct. Remember, n^2 =/ 2n in most cases.
 
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1. How can a thimble of water make a difference in the ocean?

A thimble of water may seem small, but in the vast ocean, every drop counts. The properties of matter, such as density and volume, determine how a small amount of water can still have a significant impact on the ocean's overall properties.

2. What happens to the thimble of water when it is added to the ocean?

When the thimble of water is added to the ocean, it will disperse and mix with the surrounding water. The molecules of the thimble of water will spread out and interact with the molecules of the ocean water, changing the overall properties of the ocean in that area.

3. How does the thimble of water affect the salinity of the ocean?

The addition of the thimble of water may slightly alter the salinity of the ocean in that specific location. However, the overall effect on the salinity of the entire ocean will be minimal since the amount of water is relatively small compared to the vast volume of the ocean.

4. Can the thimble of water change the temperature of the ocean?

The thimble of water may have a slight impact on the temperature of the ocean, but it is unlikely to cause a significant change. The ocean's temperature is influenced by many factors, including the sun's heat, currents, and wind, which have a much larger impact than a small amount of water.

5. How does the thimble of water affect the pH of the ocean?

The pH of the ocean is determined by the amount of carbon dioxide in the water, which can be affected by the addition of the thimble of water. However, the change in pH would be minimal and would quickly balance out with the natural processes in the ocean, such as photosynthesis by marine plants and the absorption of carbon dioxide by the ocean's surface.

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