Mass Defect - Online Tutor, Practice Problems & Exam Prep

Mass defect is a crucial concept in nuclear chemistry, representing the difference between the predicted mass of an isotope—calculated from the sum of its subatomic particles' masses—and its actual nuclear mass. Subatomic particles, namely neutrons, protons, and electrons, have masses of 1.00866 AMU, 1.00727 AMU, and 0.00055 AMU, respectively, with the bulk of an atom's mass residing in the nucleus due to the larger masses of neutrons and protons. The first law of thermodynamics states that energy cannot be created or destroyed, only transformed. This principle applies to mass defect as the mass lost during isotope formation is converted into energy, a concept mathematically expressed by Einstein's famous equation:

$E=m{c}^2$

This equation allows for the conversion between mass and energy, indicating that the predicted mass will always be greater than the nuclear mass because of this energy conversion. If the nuclear mass is not provided, it can be calculated using the nuclear mass equation: nuclear mass equals the mass number minus the number of electrons times their individual atomic mass units (0.00055 AMU for electrons). This understanding of mass defect and energy conversion is fundamental in comprehending nuclear reactions and their associated energies.

Calculating Predicted Mass

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 1.66×10-27kg.

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. They're 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 1.00866AMU, are protons weigh 1.00727AMU, and our electrons, which are the smallest, would only weigh 0.00055AMU. 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 learn how to calculate our predicted masses from these relative masses of our subatomic particles.

Mass Defect Example

Here it says calculate the predicted mass for Helium 4 isotope. I've left the relative masses of the three subatomic particles for us to utilize in terms of this example question. So helium 4. So we have 4 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 2 means that we have two protons, and here we're going to say that if we do 4 - 2, that's going to give us the number of neutrons, which is 2 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 going to say predicted mass equals 2 protons. Each one has a mass of 1.00727 + 2 neutrons. Each one has a mass of 1.00866 + 2 electrons. Each one has a mass of 0.00055. When we Add all of that together, we get a predicted mass of 4.03296 AMU. So here this would be our final answer.

Energy-Mass Conversion

Now recall that with the first law of thermodynamics, energy is not created nor destroyed, it just changes forms. Now mask defect. 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 two neutrons, 2 protons and two 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 a 2 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, 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 law says that energy cannot be created or 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. E2=mcc2. 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 can do mathematically to go between this and this. Now we're going to say as a result of being converted to mass, we're going to 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 take away 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 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 O. Keep that in mind when we're talking about energy mass conversions. There are connections to each other.

Mass Defect Example

In this example question, it says what is the mass defect in kilograms of Calcium 42 if its atomic mass is 41.958618 AMU. All right, so remember that our predicted mass minus our mass defect, which is M = R 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. Our predicted mass is counting 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 20 protons. It is neutral since it's not an ion, so the number of protons and electrons are the same. And then 42 - 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. 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 AMU. That is our predicted mass.

Take that and plug it into M. So here what do we do? We subtract this from both sides. So negative m = -0.388302 AMU. Subtract both sides by -1. So our mass defect equals 0.388302 AMU, but we want the answer to be in kilograms. Remember that one AMU is equal to 1.66 * 10^-27 KG. So here this comes out to be 6.4458 * 10^-28 kilograms as our final answer. This would be the mass defect of calcium or calcium 42.

Calculating Mass Defect

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 on by ourselves, and it's not given to us within the question. So keep this equation in mind when looking for nuclear mass.

nuclear mass = mass number - number of electrons × 0.00055

Mass Defect Example

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 going to use to find our mass defects are step one, define 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 a number of protons. It's neutral, so it also has 8 electrons. And then if we do 16 - 8, that gives us the number 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. We'd multiply them each by their atomic mass unit and add up the totals together, right?

So for a proton it would be 8 * 1.00727 AMU, an electron is 8 * 0.00055 AMU, and for our neutron it's 8 * 1.00866 AMU. When we do all of that, our predicted mass comes out to be 16.13184 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 0.00055 AMU. So that's 15.9956 AMU.

And then here use the calculated mass of step one and step 2 to determine the mass defect. 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 0.13624 AMU. Divide both sides by -1. So our mass defect M equals 0.13624 AMU, so that will be our final answer for the isotope of oxygen 16.

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). 

¹⁴C

• A. 3.1789 x 10^–22 mg
• B. 1.9837 x 10^–22 mg
• C. 1.0294 x 10^–20 mg
• D. 1.5123 x 10^–21 mg

Here’s what students ask on this topic:

How do you calculate mass defect?

Mass defect is the difference between the calculated mass of an atom's constituent protons, neutrons, and electrons and its actual mass as measured experimentally. To calculate mass defect, you follow these steps:

1. Determine the number of protons and neutrons in the nucleus of the atom. You can find this information on the periodic table of elements, where the atomic number represents the number of protons and the difference between the mass number and the atomic number gives you the number of neutrons.
2. Calculate the total mass of the protons, neutrons, and electrons if they were separate. Use the standard atomic mass units: a proton has a mass of approximately 1.007276 amu, a neutron has a mass of approximately 1.008665 amu, and an electron has a mass of approximately 0.0005486 amu.
3. Multiply the number of each particle by its respective mass to get the total mass for each type of particle, then sum these values to get the total calculated mass.
4. Obtain the actual atomic mass of the atom (isotope) from the periodic table or a reliable scientific resource.
5. Subtract the actual mass from the total calculated mass of the individual nucleons and electrons. This difference is the mass defect.

$\text{Mass Defect}=\left(\text{Total Calculated Mass}\right)$

What action results in the mass defect?

The mass defect is a result of the binding energy that holds the nucleus together in an atom. When protons and neutrons, which are the nucleons, come together to form a nucleus, they are bound by the strong nuclear force. This force is incredibly powerful, and it works to overcome the repulsion between the positively charged protons.

To maintain this binding, a certain amount of energy is required, known as the binding energy. According to Einstein's famous equation, $E^2=\mathrm{mc}{2}^{}$, energy and mass are interchangeable. This means that the binding energy has an equivalent mass. When nucleons bind together, the energy that's converted to bind them results in a loss of mass. This loss is what we refer to as the mass defect.

The mass defect is not a loss in the usual sense; the 'missing' mass has been converted into binding energy to hold the nucleus together. This is why the mass of a nucleus is always less than the sum of the masses of its individual protons and neutrons.

What does the mass defect measure?

The mass defect measures the difference between the sum of the individual masses of protons, neutrons, and electrons that make up an atom's nucleus and the actual mass of the nucleus itself. This discrepancy arises because some of the mass is converted into binding energy, which holds the nucleus together, according to the mass-energy equivalence principle expressed by Einstein's famous equation:

E² = mc²

When nucleons (protons and neutrons) bind together to form a nucleus, the mass defect is a manifestation of the energy released during this process. The larger the mass defect, the more stable the nucleus is, as it indicates a greater amount of binding energy. This concept is crucial in nuclear physics and has practical applications in areas such as nuclear energy and nuclear weapons development.