8 million uranium atoms in milligrams?

[paulhunn]

Where i live in the UK all the A-level students have just had their results. It has been said on the news that a new A* level will be added to the A levels to differentiate between the bright and the very bright and that an example of an A* question would be: 8 million uranium atoms in milligrams.
Just wondering how you would go about working this out. The way i thought it would be done is by working out the weight of an individual atom by proton, neutron number etc and multiplying by 8 million. The only problem is i have no idea how much a proton or neutron weighs or how to convert the impossibly small mass to a metric measurement.
I would be very grateful to anyone who can shed any light on the matter

Paul

 

[WhyIsItSo]

From http://www.bartleby.com/65/at/atomMasU.html

An Atomic Mass Unit $$\approx 1.66*10^{-24}$$grams
$$\approx 1.66*10^{-21}$$milligrams

I see Uranium (U) has an atomic mass of 238.07, so...

$$8*10^6 * 238.07 * 1.66*10^{-21} = 3.1615*10^{-12}$$

Therefore 8 million uranium atoms weighs approximately $$3.1615*10^{-12}$$ milligrams.

 

[paulhunn]

Thanks for the relpy. I understand it now

Paul

 

[sdekivit]

Another way would be the use of Avogadro's number.

 

[Gelsamel Epsilon]

From http://www.bartleby.com/65/at/atomMasU.html

An Atomic Mass Unit $$\approx 1.66*10^{-24}$$grams
$$\approx 1.66*10^{-21}$$milligrams

I see Uranium (U) has an atomic mass of 238.07, so...

$$8*10^6 * 238.07 * 1.66*10^{-21} = 3.1615*10^{-12}$$

Therefore 8 million uranium atoms weighs approximately $$3.1615*10^{-12}$$ milligrams.

I think you're overcomplicating this.

238.07g = 1 Mol of Uranium, so 237.07/(6*10^23) = 1 Uranium Atom

So (237.07*(8*10^6))/(6*10^23) = the amount he wants. Which is 3.16093333*10^-15 grams or 3.16093333*10^-12 milligrams (give or take a bit, because it's actually 6.022*10^23).

It's much more simple, and you can figure it out with elementary chemistry knowledge.