Why is the amu of chlorine-35 less than 35? [duplicate]

My book says that a proton weighs 1.0073u, a neutron weighs 1.0087u, and an electron weighs 0.00055u.

Now, why is the mass of chlorine-35 equal to 34.969? Are there not 17 protons, 18 neutrons, and 17 electrons? I calculated it and it sums to around 35.29. Where did I go wrong?

• It did not go wrong. The average mass per nucleon decreases toward iron, and then increases toward uranium. Where do you think nuclear fusion and fission take their energy from ? Check masses of 4He and 16O, or Fe isotopes. – Poutnik Apr 20 at 5:02
• hi! my book said that all protons are the same weight, so goes with neutrons and electrons. where did i go wrong when I simply added the weights? – 12345bird Apr 20 at 5:05
• You have not counted mass loss due their bound energy. $\Delta E = \Delta m \cdot c^2$ – Poutnik Apr 20 at 5:07
• oh cool! my book did not teach about that yet, so good to know. Thanks for helping me! :) – 12345bird Apr 20 at 5:08
• Related question and answer. – Nicolau Saker Neto Apr 20 at 5:10

You need to account for the energy released when nucleons and electrons come together and form a Cl-35 atom. Its called the Binding Energy.

This sort of equation can help to explain :

(Rest Mass Energy of Individual nucleons,electrons*) - (Various Binding Energies) = (Rest Mass Energy of Natural)

*edit

• ok thanks! i get it now, since the book did not say anything about binding energy. – 12345bird Apr 20 at 5:10
• Also, I used the term mass-energy. You can interpret it as actual mass, according to the mass-energy equivalence ( the famous E=mc^2 ). – Potter Apr 20 at 5:13
• @12345bird As mass of subatomic particles is used to be expressed in equivalent units of energy, usually MeV. – Poutnik Apr 20 at 5:26
• should be: (Rest Mass Energy of Individual particles, neutons, protons and electrons) - (Various Binding Energies) = (Rest Mass Energy of Natural Nucleus) // The electron binding energies are small compared to the nuclear binding energies, but easily measurable today. – MaxW Apr 20 at 6:08
• Oh noted, I'm not really up to date on new technologies. I'll make the appropriate edit. Thanks! – Potter Apr 20 at 7:17