Atomic Mass: Helium-4 Nucleus Contribution

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Discussion Overview

The discussion revolves around the calculation of the fraction of mass contributed by the nucleus of a helium-4 atom, considering the masses of its electrons and the nucleus. Participants explore the implications of significant figures and the accuracy of provided mass values.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant presents a formula for calculating the fraction of mass contributed by the nucleus, but expresses uncertainty about the mass of neutrons and the density required for the calculation.
  • Another participant calculates the mass of the atom and the fraction of mass but questions the accuracy of the provided mass values, suggesting that the mass of electrons should not exceed that of protons.
  • A later reply corrects the mass of electrons, indicating that the notation should include scientific notation (e.g., "e-28") to reflect the correct scale.
  • Some participants express skepticism about the precision of the mass values given, questioning the validity of having such precise measurements (12 significant figures).
  • One participant acknowledges a mistake in their understanding of the mass of the nucleus and suggests a corrected approach to finding the mass of the nucleus by subtracting the mass of the electrons from the mass of the atom.
  • Another participant points out that the mass values provided do not correspond to known values for protons or nuclei, indicating a potential misunderstanding of the data.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the accuracy of the mass values provided or the correct approach to calculating the fraction of mass contributed by the nucleus. Multiple competing views and corrections are presented throughout the discussion.

Contextual Notes

Limitations include potential errors in the provided mass values, the need for scientific notation to accurately represent the masses, and unresolved issues regarding significant figures in the calculations.

AryaUnderfoot
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Homework Statement


The mass of a helium-4 atom is 6.64648310224 g, and each of its two electrons has a mass of 9.10939310228 g. What fraction of this atom’s mass is contributed by its nucleus?

Homework Equations


fraction of mass = mass of nucleus/mass of atom

The Attempt at a Solution


I suppose I should calculate the mass of nucleus first. But I only have the mass of the electrons, no mass of neutron, also no density...
 
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Mass of nucleus = 6.64648310224
Mass of electrons = 9.10939310228 * 2
Mass of atom = 9.10939310228 * 2 + 6.64648310224 = 24.8652693068

Fraction of mass = mass of nucleus/mass of atom = 6.64648310224/24.8652693068 = 0.26729986392797124965341901615185

But the only problem is your data.
The masses of electron is not more than that of proton. And the mass of proton is too much.
I think you forgot to multiply the masses with power of 10s.
Well, this is the solution. Solve it in this way after you correct the data.
 
AryaUnderfoot said:
9.10939310228 g

That's incorrect on at least two accounts. First, digits after 9.1093 are wrong, second, the end should read not "28" but "e-28" - and this "e-" is what makes the most important difference.
 
Where is this question from? I find it hard to believe that these masses are known to anything like 12 significant figures.
 
epenguin said:
Where is this question from? I find it hard to believe that these masses are known to anything like 12 significant figures.

9.10938356(11)×10−31 kg, if you copy digits only you will get even 13 sigfigs :wink:
 
Aryamaan Thakur said:
Mass of nucleus = 6.64648310224
Mass of electrons = 9.10939310228 * 2
Mass of atom = 9.10939310228 * 2 + 6.64648310224 = 24.8652693068

Fraction of mass = mass of nucleus/mass of atom = 6.64648310224/24.8652693068 = 0.26729986392797124965341901615185

But the only problem is your data.
The masses of electron is not more than that of proton. And the mass of proton is too much.
I think you forgot to multiply the masses with power of 10s.
Well, this is the solution. Solve it in this way after you correct the data.
Ohh! I did a mistake
I thought 6.64648310224 is the mass of nucleus.

Correcting it!
Now,
Mass of nucleus = mass of atom - mass of electrons
And after you find it divide it with the mass of atom.

I hope you've verified the data.
 
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10-27 kg is not the mass of the proton nor any nucleus.
 
Aryamaan Thakur said:
Ohh! I did a mistake
I thought 6.64648310224 is the mass of nucleus.

Correcting it!
Now,
Mass of nucleus = mass of atom - mass of electrons
And after you find it divide it with the mass of atom.

I hope you've verified the data.
Ah, my bad. I forgot the significant number behind the values..I got it now. Thanks!

And also sorry for late reply ^^
 

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