Now, before we can talk about mass defect, it's first important that we are able to determine our predicted mass. Now, our predicted mass represents the mass of all subatomic particles within a given element. The number of neutrons protons and electrons now recall that one atomic mass unit is equal to 1.66 times 10 to the negative 27 kg. Doing this helps us to find a relative mass in atomic mass units for each one of our subatomic particles. Now remember we have our neutrons protons and electrons, their actual masses and kilograms are these values. And by utilizing this conversion factor, we can find their relative masses doing this. We'd see that our neutrons weigh 1.00866 AM U. Our protons weigh 1.00727 AM us. And our electrons which are the smallest would only weigh 0.00055 AM U. As we can see, the neutrons are just slightly larger or have slightly greater masses than our protons and their masses are much greater than our electrons. That's why a vast majority of the total mass of an atom is found within the nucleus where the protons and neutrons reside. Right. So we're gonna learn how to calculate our predicted masses from these relative masses of our subatomic particles.

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example

Mass Defect Example

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Here it says, calculate the predicted mass for helium four isotope. I've left the relative masses of the three subatomic particles for us to utilize in terms of this example question. So helium four. So we have four for the mass number looking on the periodic table, helium has an atomic number of two. Now, here it's mass. Well, it's atomic number being two means that we have two protons. And here we're going to say that if we do four minus two, that's gonna give us the number of neutrons, which is two as well. Here we're doing dealing with an isotope, not an ion. So if we're not dealing with an ion, that means the number of protons and electrons are the same. So we also have two electrons with all of this, we can determine our predicted mass. So we're gonna say predicted mass equals two protons. Each one has a mass of 1.00727 plus two neutrons. Each one has a mass of 1.00866 plus two electrons. Each one has a mass of 0.00055. When we add all of that together we get a predicted mass of 4.03296 AM U. So here, this would be our final answer.

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concept

Energy-Mass Conversion

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Now recall that with the first law of thermodynamics energy is not created nor destroyed, it just changes forms. Now mass defect, we're gonna say that is lowercase M this is just the mass lost from combining subatomic particles in the formation of an isotope. If we take a look here at this image here, we're talking about two neutrons, two protons and two electrons combining together, their overall mass is 4.03296 AM U. That is their predicted mass, all of them together in this process of them combining together. Something bizarre happens. There's actually a deletion or loss of mass of them combining the mass that's lost or minus the mass. The mass comes out to this value. This mass is related to the mass defect. These subatomic particles combining together is what gives us our isotope. In this case, helium four. Here, the nucleus has a two protons and two neutrons together and orbiting that are two electrons. Now, here we also have energy on the right side recall that bomb formation involves the releasing of energy, which is why it's on the right side of the equation. But here this equation can be seen going either way here, we're looking at it going this way, we could also look at it going the reverse way. See in the opposite direction, this energy could be used to basically attack or get involved with the isotope, breaking it back into its individual subatomic particles. So in this case, energy is absorbed to break up the isotope. So our predicted mass of all the isotopes together is this number. But our nuclear mass is this number. The nuclear mass represents your actual mass. This is the mass that you find on the periodic table for that element, the atomic mass. Now, if we take a look at this, what this image is saying is that our predicted mass minus our mass loss, which is the mass defect equals our nuclear mass plus energy. Remember first loss says that energy cannot be created nor destroyed. It just changes forms this loss of mass is actually converted into this energy here on the product side. And we just said that we can go forward or backwards. Mathematically, how is that possible? It's possible through this equation on the bottom. Some of you might have already noticed it E equals MC squared. We know that Einstein is connected to this equation. This equation allows us to go between energy and mass. If you know the energy involved, you can determine the mass. If you know the mass involved, you can determine the energy they're interconnected to one another. OK. So this equation is what we can do mathematically to go between this and this. Now we're gonna say as a result of being converted to mass, we're gonna say the predicted mass is always greater than the nuclear mass. So remember predicted mass minus your mass defect equals your nuclear mass. That's the takeaway from this plus the energy. But we don't worry about that here. We're talking about these because these deal with weight mass, OK. Energy is its own separate thing, different units. OK. So this is what we need to take away from this image. In the combining of subatomic particles. We don't expect all of that mass to be converted into the newly formed isotope. Some of it's gonna be lost and converted into energy in this process. That same energy could then be reinvested back into the isotope if we wish to break it up into its original subatomic particles. So keep that in mind when we're talking about energy, mass conversions their connections to each other.

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example

Mass Defect Example

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In this example question, it says, what is the mass defect in kilograms of calcium? 42 if its atomic mass is 41.958618 AM U? All right. So remember that our predicted mass minus our mass defect, which is M equals our nuclear mass, which is our atomic mass. So we already know our, our atomic mass is 41.958618 AM U. We're looking for a mass defect M to be able to find that we need to calculate our predicted mass. So our predicted mass is counting up all the masses of the subatomic particles comprised within calcium 42. So calcium 42 we have 42 as its mass number. Its atomic number is 20. Here 20 would relate to it 20 protons, it is neutral since it's not an ion. So the number of protons and electrons are the same and then 42 minus 20 gives us the number of neutrons which is 22. So here we'd say our predicted mass comes from multiplying each of these by their AM U value. OK. So this is the weight of each one of these subatomic particles. So we multiply them by their masses and then we add up all the totals together. When we do that, we get 42.34692 AM U. So that is our predicted mass take that and plug it in 2 a.m. Yeah. So here what do we do? We, we subtract this from both sides. So negative M equals negative 0.388302 AM U subtract both sides by minus one. So our mass defect equals 0.388302 AM U but we want the answer to be in kilograms. Remember that 1 a.m. U is equal to 1.66 times 10 to the negative 27 kilograms. So here this comes out to be 6.4458 times 10 to the negative 28 kg as our final answer. So this would be the mass defect of calcium or calcium. 42.

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concept

Calculating Mass Defect

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Now, if the nuclear mass of an isotope is not given, then more extensive calculations will be needed to calculate the mass defect. Here, we're gonna say in these instances, nuclear mass is the difference between the mass number of the isotope and the mass of all of its electrons. Now, here we'd say that our nuclear mass equation is nuclear mass which again is the atomic mass of the isotope equals its mass number minus the number of electrons times their individual atomic mass units. Remember for electrons that's equal to 0.00055. So this is the equation we utilize if we have to calculate nuclear mass on by ourselves, and it's not given to us within the question. So keep this equation in mind when looking for nuclear mass.

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example

Mass Defect Example

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Here in this example question, it says calculate the mass defect in atomic mass units for oxygen 16. Here we're given the atomic mass units for each of the three subatomic particles. Now, the steps that we're gonna use to find our mass defects are step one to find predicted mass, find the number of subatomic particles within the isotope and add their masses together. So here we're talking about oxygen, 16 oxygen has an atomic number of eight, eight represents a number of protons, it's neutral. So it also has eight electrons. And then if we do 16 minus eight, that gives us the number of, of neutrons, which is also eight. So we have eight across the board for our three subatomic particles here is each one of their atomic mass units. So we'd multiply them each by their atomic mass unit and add up the totals together, right? So for protons be 18 times 1.00727 AM U, an electron is eight times 0.00055 AM U. And for our neutron, it's eight times 1.00866 AM us when we do all of that, our predicted mass comes out to be 16.13. And we're gonna say 184 emu So step two to find the nuclear mass, you're gonna subtract the mass number by the combined mass of all the electrons. So the mass number is 16 for oxygen, 16 and B minus are eight electrons. Each one of them having a mass of 0.00055 AM U. So that's 15.9956 AM U. And then here use the calculated mass of step one and step two to determine the mass defect. So remember predicted mass minus our mass defect equals our nuclear mass. So just plug it in. It's all for M. So predicted is 16.13184. And then nuclear is 15.9956 subtract 16.13184. So here we're gonna get negative M equals negative 0.13624 A U divide both sides by minus one. So our mass defect M equals 0.13624 AM U. So that will be our final answer for the isotope of oxygen. 16.

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Problem

Problem

Calculate the mass defect (in mg) for the following isotope. (1 neutron = 1.00866 amu, 1 proton = 1.00727 amu, & 1 electron = 0.00055 amu).