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 kilograms. Doing this helps us to find the 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 in 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 amu, Our protons weigh 1.00727 amus, and our electrons, which are the smallest, would only weigh 0.00055 amu. 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 going to 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 4 isotope. I've left the relative masses of the 3 subatomic particles for us to utilize in terms of this example question. So helium-four. So we have 4 for the mass number. Looking on the periodic table, helium has an atomic number of 2. Now here its mass, well its atomic number being 2 means that we have 2 protons. And here we're going to say that if we do 4 minus 2 that's going to give us the number of neutrons which is 2 as well. Here we're 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 2 electrons. With all of this, we can determine our predicted mass. So we're gonna say predicted mass equals 2 protons, each one has a mass of 1.00727 plus 2 neutrons, each one has a mass of 1.00866, plus 2 electrons, each one has a mass of 0.00055. While we add all of that together, we get a predicted mass of 4.03296 amu. 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, mask effect, we're going to 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 2 neutrons, 2 protons and 2 electrons combining together. Their overall mass is 4.03296 amu. 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, so 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 4. Here the nucleus has 2 protons and 2 neutrons together, and orbiting that are our 2 electrons. Now, here we also have energy on the right side. Recall that bond 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. Seeing 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 law 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 m c 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. Okay. 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. Okay. Energy is its own separate thing, different units. Okay. 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 going to 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 41.958 618 AMU. Alright, 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 atomic mass is 41.958618 amu. 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 forty two, we have 42 as its mass number, its atomic number is 20. Here 20 would relate to its 20 protons, it is neutral since it is not an ion, so the number of protons and electrons are the same, and then 42 minuteus 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 amu value. Okay. 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 point 34692 AMU. So that is our predicted mass. Take that and plug it in to AMU. So here, what do we do? We we subtract this from both sides, So negative m equals negative 0.388 302amu. Subtract both sides by -one, so our mass defect equals 0.388302amu, but we want the answer to be in kilograms. Remember that 1 amu is equal to 1.66 times 10 to the negative 27 kilograms. So here this comes out to be 6.4458x10-twenty 8 kilograms 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 going to 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 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 3 subatomic particles. Now the steps that we're going to use to find our mass defects are step 1, 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 8. 8 represents the number of protons. It's neutral, so it also has 8 electrons. And then if we do 16 minuteus 8, that gives us the number of neutrons, which is also 8. So we have 8 across the board for our 3 subatomic particles. Here is each one of their atomic mass units, so we multiply them each by their atomic mass unit, and add up the totals together. Right? So for a proton to be 8 times 1.00727 0.00055 amu, and for our neutron it's 8 times 1.00866 amus. When we do all of that, our predicted mass comes out to be 16.13, and we're going to say 184 AMU. So step 2, to find the nuclear mass you're going to subtract the mass number by the combined mass of all the electrons. So the mass number is 16 for oxygen, 16, and we minus our 8 electrons, each one of them having a mass of point 00055 amu. So that's 15.9956 amu. And then here use the calculated mass of step 1 and step 2 to determine the mass defect. So remember, predicted mass minus our mass defect equals our nuclear mass. So just plug it in and solve for m. So predicted is 16.13184, and then nuclear is 15.9956. Subtract 16.13184. So here we're going to get negative m equals negative 0.136 24amu. Divide both sides by -one, so our mass defect m equals 0.13624 amu. 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).