Where does 1u = 1.661x10^-24g come from?

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A carbon atom has 6 protons and 6 neutrons.
This equals 12.000u & 1u is one-twelfth the mass of an atom of carbon.
1u =1.661x10^-24g
so 6 protons plus 6 neutrons should equal the carbon-12 atom in grams
and this divided by 12 should equal 1u =1.661x10^-24g
proton weight in grams (1.672622 x 10^-24g)
neutron wight in grams (1.674927 x 10^-24g)
1.672622 x 6
+ 1.674927 x 6
-------------------
20.085294g
divide this by 12 = 1.67 x 10^-24g

I wonder whether i am doing something wrong or my numbers are inaccurate but this can't be as in the book it mentons 1.661x10^-24g right before it gives the proton and neutron masses, can someone explain how 1.661x10^-24g is achieved and is 20.085294g (the answer i got before i divided though you'd include1.661x10^-24g appropriately) the real mass of the carbon atom.

Thanks so much (first post

 

[mgb_phys]

Not entirely sure what you are asking but.

The atomic mass unit (u) = 1.660538782×10⁻²⁷ kg (or 10^-24g)
A proton has a mass of 1.672621637×10⁻²⁷ kg and a neutron 1.67492729×10⁻²⁷

The mass of the nucleus of an atom is slightly less than the mass of it's neutrons and protons because of the binding energy that holds the nucleus together - effectively the mass of a proton and neutron depends on where it is.

Incidentally there is nothing special about Carbon - it's just a convenient substance to work with and naturally occurring fossil carbon is almost pure C12.

 

[Borek]

Google mass deficit.

 

[sponsoredwalk]

1.661x10^-24g = 1u
How is this number achieved and what is it?
Every site i go to just dictates that you use this number, and my book says that it is a conversion factor, but i have no intuitive grasp of it.

(from above message)
The mass of the nucleus of an atom is slightly less than the mass of it's neutrons and protons because of the binding energy that holds the nucleus together - effectively the mass of a proton and neutron depends on where it is.

Does this mean that my method of adding up all the protons and neutrons and dividing by twelve is true, and that the margin of error is due to binding energy?

 

[mgb_phys]

1.661x10^-24g = 1u
How is this number achieved and what is it?

It's 1/12 the mass of a Carbon atom.
The original idea was that it was the average mass of proton/neutron but that was before relativity+binding energy was discovered.
But to within a % or so it still is - so it's useful for chemistry.

To measure it you simply weigh some carbon and count how many atoms there are !
This depends on measuring Avagadro's constant - the number of Carbon atoms in 12g of Carbon.

There is an attempt to turn the whole thing around and define the Kg based on this by very accurately counting how many atoms there are in a Silicon sphere (silicon chosen rather than carbon for practical reasons)

Does this mean that my method of adding up all the protons and neutrons and dividing by twelve is true, and that the margin of error is due to binding energy?

Correct.

 

[sponsoredwalk]

Thanks for the help, yes i guess relativity would affect it but i have just discovered something further and i am curious how it relates to everything;

hydrogens molar mass is 1g, (6.02 x 10^23 hydrogen atoms have a mass of 1g)
the molecular mass of a Hydrogen atom is 1/6.02 x 10^23 = 1.66 x 10^-24g

That is weird ^^^

And why does it take 32.066g of Sulfur to = 1 mole? 6.02 x 10^23
Why 118.71g on Tin = 1 mole,

Is this due to the huge difference in the sizes of the atoms in each of these different elements? I don't think there is a huge difference...

 

[mgb_phys]

Non-integer atomic masses are generally because the natural substance contains a mix of isotopes
eg Chlorine is 35.5 because it's about 75% Cl₃₅ and 25% Cl₃₇, so a mole of natural Chlorine would weigh 35.5g ( actually 35.453g )

Hydrogen is about 150ppm Deuterium, with a mass of 2, so chemical hydrogen has an average mass of slightly more than 1.

 

[Borek]

Is this due to the huge difference in the sizes of the atoms in each of these different elements? I don't think there is a huge difference...

You have just learned you thought wrong