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

  • Thread starter Thread starter sponsoredwalk
  • Start date Start date
Click For Summary

Discussion Overview

The discussion centers around the origin and understanding of the atomic mass unit (1u = 1.661x10^-24g), particularly in relation to carbon-12 and the implications of binding energy on atomic mass calculations. Participants explore the definitions, measurements, and conceptual underpinnings of atomic mass in the context of chemistry and physics.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant states that 1u is defined as one-twelfth the mass of a carbon-12 atom, leading to the value of 1.661x10^-24g.
  • Another participant mentions that the mass of a nucleus is less than the sum of its protons and neutrons due to binding energy, suggesting that this affects the accuracy of simple mass calculations.
  • A participant questions the intuitive understanding of the conversion factor 1u = 1.661x10^-24g, seeking clarity on its derivation.
  • It is noted that the original idea of atomic mass was based on average proton/neutron mass, but this has evolved with the understanding of relativity and binding energy.
  • One participant discusses the relationship between molar mass and atomic mass, using hydrogen as an example, and raises questions about the consistency of atomic masses across different elements.
  • Another participant explains that non-integer atomic masses arise from the presence of isotopes in natural substances, using chlorine as an example.

Areas of Agreement / Disagreement

Participants express varying levels of understanding regarding the calculation of atomic mass and the implications of binding energy. While some points are clarified, there remains uncertainty and differing interpretations of how atomic mass is derived and its implications across different elements.

Contextual Notes

Participants highlight limitations in their calculations due to assumptions about binding energy and the isotopic composition of elements, which may affect the accuracy of mass estimates.

Who May Find This Useful

This discussion may be of interest to students and enthusiasts of chemistry and physics, particularly those exploring atomic theory, mass calculations, and the implications of isotopes in atomic mass measurements.

sponsoredwalk
Messages
531
Reaction score
5
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:))
 
Physics news on Phys.org
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.
 
Google mass deficit.
 
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?
 
sponsoredwalk said:
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.
 
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...
 
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.
 
Last edited:
sponsoredwalk said:
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 :wink:
 

Similar threads

Calculating the weight of 1 atomic mass unit
  • · Replies 29 ·
Replies
29
Views
8K
How Does Atomic Mass Number Determine Both Nucleus Composition and Molar Mass?
  • · Replies 6 ·
Replies
6
Views
8K
Off by order of magnitude when calculating how much calcium is in bone
  • · Replies 8 ·
Replies
8
Views
2K
Verify that the number of atoms Avagadro's constant
  • · Replies 3 ·
Replies
3
Views
3K
How Does Fossil Fuel Combustion Impact Atmospheric CO2 Concentration Annually?
  • · Replies 6 ·
Replies
6
Views
7K
Atomic displacements, replacements, and radiation damage of structural materials
  • · Replies 1 ·
Replies
1
Views
2K
Alpha particle and Beryllium reaction
  • · Replies 3 ·
Replies
3
Views
4K
Kinetic Energy for particles (alpha decay)
  • · Replies 2 ·
Replies
2
Views
3K
Stability of a White Dwarf Against Gravitational Collapse
  • · Replies 3 ·
Replies
3
Views
2K
Neutron, proton collision problem
  • · Replies 5 ·
Replies
5
Views
6K