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So I tried to calculate the relative mass of a lithium-7 atom. I added up the masses of all the protons, neutrons and electrons, like this: mass = relative mass of 3 protons + relative mass of 4 neutrons + relative mass of 3 electrons = 3 + 4(1838.68/1836.15) + 3(1/1836.15) = 7.007145386 However, our bound atom would have a lower mass than this. Our chemistry book states the relative mass of a lithium-7 atom as 7.016, which is greater than our estimation. Where des this "extra" mass come from, then? I mean, other than the particles themselves.

Zamil Hoque Siddique
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  • Yes, but why is that? That is what I am asking. – Zamil Hoque Siddique Jan 26 '22 at 06:07
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    The mass of atoms cannot be calculated by addition of masses of free particles. Additionally, the mass of proton is not the relative unit of atomic mass, but 1/12 of 12C is. Mass of 4He is about 0.7% less then mass of 2p + 2n + 2e. The difference is the equivalent mass of released nuclear bonding energy. – Poutnik Jan 26 '22 at 06:10
  • I don't quite follow your calculation either. Using CODATA values for particles' masses, I arrive at a different theoretical number for $\ce{^7Li}$: $$3\times\pu{1.0072 u} + 4\times\pu{1.0087 u} + 3\times\pu{0.0005 u} = \pu{7.0579 u}$$ – andselisk Jan 26 '22 at 06:28
  • The good initial step before asking is reading relevant textbooks, googling keywords and studying the search results. This prevents cases of asking for answers that have been already written in many ways on many places. The Google search scope can be eventually limited to the particular address domain by adding the additional term e.g. site:stackexchange.com, site:libretexts.org or site:wikipedia.org . // Review also Chemistry SE: resources-for-learning-chemistry – Poutnik Jan 26 '22 at 07:04
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    Your calculation incorrectly assumes that the mass of a proton is 1 u. All other masses used are given relative to this incorrect proton mass. Basically, you have correctly calculated that sum of the individual components of the Li-7 atom is 7.0071 times heavier than a free proton, but now you have to multiply this by the actual mass of a free proton (1.0072 u), which yields 7.0576 u, in good agreement with andselisk's more precise value. Now this value is larger than the true mass of a Li-7 atom, due to release of nuclear (and electronic) binding energy when you join the particles together. – Nicolau Saker Neto Jan 26 '22 at 07:10
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    Now i get why I was wrong. I was using masses relative to the mass of a proton. But relative isotopic masses are measured in Daltons. That's why my calculation didn't match. I did it the correct way now (considering binding energy too) and now it works. Thanks. – Zamil Hoque Siddique Jan 26 '22 at 07:13

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