Calculating the rest mass of Ra [simple ]

[bsmm11]

Calculating the rest mass of Ra [simple!]

Homework Statement

Calculate the rest mass of 226/88 Ra.

Homework Equations

The Attempt at a Solution

There are 88 protons and 138 neutrons.
Therefore, (88*1.007276)+(138*1.008665)=227.8361u
But the answer says 226.0254u.
It also says 4/2 He is 4.0026u while my calculation is 4.0319u.

HELP~

 

[Curious3141]

Homework Statement

Calculate the rest mass of 226/88 Ra.

Homework Equations

The Attempt at a Solution

There are 88 protons and 138 neutrons.
Therefore, (88*1.007276)+(138*1.008665)=227.8361u
But the answer says 226.0254u.
It also says 4/2 He is 4.0026u while my calculation is 4.0319u.

HELP~

The measured mass of an intact atomic nucleus is generally less than the masses of the individual nucleons (neutrons and protons) added together. The difference is called a "mass defect", and it's the result of "binding energy" that was radiated out and lost during creation of the atomic nucleus. The loss of that energy leads to a lowering of the potential energy of the bound nucleus, and therefore a more stable state (that needs an input of energy to break it up again). The binding energy is related to the mass defect by E = mc^2, so even a small mass defect leads to a large figure for the binding energy (c^2 is a large factor).

So it's to be expected that the mass of the whole nuclei are slightly lower than you calculated. What I can't figure out is how you're supposed to "calculate" the mass of the nuclei, since I thought that those are usually empirically measured (and the mass defect, and binding energy are the calculated quantities).