Isotopes - Online Tutor, Practice Problems & Exam Prep

Isotopes are atoms of the same element that differ in the number of neutrons, leading to varying mass numbers while maintaining the same atomic number. For example, carbon has three isotopes: carbon-12, carbon-13, and carbon-14, with mass numbers of 12, 13, and 14, respectively. Radioactive isotopes, like carbon-14, are unstable and decay over time, emitting energy and particles. Their decay rate is measured by half-life, crucial for applications in medicine and radiometric dating of fossils.

Isotopes

Alright. So now that we've covered the basics of the atom, in this video we're going to introduce isotopes. All atoms of the same element are going to have the same number of protons because if you change the number of protons, you're going to change the element. Once again, all atoms of the same element will have the same number of protons. However, all atoms of the same element do not necessarily have the same number of neutrons, and so the number of neutrons can vary between atoms of the same element. This is exactly what leads us to this idea of isotopes.

Isotopes are defined as atoms of the same element that only vary in the number of neutrons. Isotopes always have the same atomic numbers, which means that they're going to have the same number of protons. If you change the number of protons, you change the element. Therefore, all isotopes have the same atomic number or the same number of protons but do not have the same number of neutrons. This means that they will have different mass numbers, which is the total number of protons and neutrons.

The reason isotopes have different mass numbers is because they have different neutrons. If you have a varying number of neutrons, you're automatically going to vary in the mass number. Recall from our previous lesson videos that we defined atomic number and mass number, but we also defined the atomic mass, which is the average mass of all the isotopes that exist for a particular element. Let's take a look at our example down below to look at the atomic mass of carbon's 3 isotopes.

The first isotope is here, the second is here, and the third is right here. One thing to note about these three isotopes of carbon is that they all have the same exact number of protons, 6, and that is once again going to be the atomic number. Notice that these scenarios also have the same exact number of electrons. The electrons do not vary between these scenarios. Thus, the only thing that differs between these scenarios is going to be the total number of neutrons, which we have here in the middle. When you count the neutrons in the nucleus of the first one, there are 6 neutrons. In the second, there are 7 neutrons, and in the third, there are 8 neutrons. These scenarios only differ from each other in the total number of neutrons in the nucleus, which is what makes them isotopes.

If we want to calculate the mass number for each of these isotopes, we total up the number of protons and neutrons. For the first atom, add 6 protons to 6 neutrons, giving us a mass number of 12, referred to as a carbon-12 atom, abbreviated as ₆C¹². For the second isotope, 6 protons plus 7 neutrons give us 13, abbreviated as ₆C¹³. For the third isotope, summing 6 protons and 8 neutrons results in a mass number of 14, hence it is a carbon-14 atom, abbreviated as ₆C¹⁴.

The abundance of these isotopes also differs. The first isotope makes up about 99% of all carbon atoms, with only 1% of all carbon atoms being these other two isotopes. Therefore, the mass of these other isotopes has a very small impact on the average mass of all the isotopes. Considering 100% of these carbon atoms, the average atomic mass is close to the mass number of the most abundant isotope, hence it's 12.011. The .011 arises from the small percentage of isotopes that are slightly heavier than 12.

This here concludes our introduction to isotopes, and we'll be able to get some practice as we move along through our course. So I'll see you all in our next video.

What is TRUE about carbon-13 and carbon-14?

• A. They are isotopes.
• B. They have the same mass number.
• C. They have the same number of neutrons in their nuclei.
• D. They behave differently in biological reactions.
• E. None of the above are true.

How are Carbon-13 and Nitrogen-15 respectively different from the more abundant isotopes Carbon-12 and Nitrogen-14? Carbon-13 and Nitrogen-15 _______________:

• A. Each have an extra neutron.
• B. Each have an extra proton.
• C. Each have one less neutron.
• D. Each have one less proton.
• E. Each have one less electron.

The atomic number of nitrogen is 7. Nitrogen-15 has a greater mass number than nitrogen-14 because the atomic nucleus of nitrogen-15 contains ________.

• A. 7 neutrons.
• B. 8 neutrons.
• C. 8 protons.
• D. 15 protons.

Radioactive Isotopes

Alright. So now that we've introduced isotopes in this video, we're going to talk a little bit about radioactive isotopes. And so radioactive isotopes are really just defined as isotopes themselves that are really, really unstable and break down over periods of time by emitting energy in the form of rays or particles. And so if we take a look at our image down below over here on the left-hand side, notice that we're showing you an example of the radioactivity of a carbon 14 isotope. And so this here represents the nucleus of the radioactive atom, more specifically, the nucleus of the carbon 14 isotope, which we know from our last lesson video is going to have a total of 6 protons in its nucleus and a total of 8 neutrons in its nucleus since its mass number is 14.

Now carbon 14 is a radioactive isotope, meaning that it is really really unstable and will break down over time by emitting energy in the form of rays or particles. And so this arrow right here represents released energy, and this arrow down here represents released subatomic particles. And so once again, this radioactive atom is going to decay and break down over time. Now the rate that radioactive atoms break down is pretty consistent, and so from that consistency scientists can calculate what's known as the half-life. The half-life is defined as the exact amount of time it takes for exactly half of all radioactive atoms in a sample to break down.

And so these radioactive isotopes actually have several important uses in human life, and so for example radioactive isotopes are used in medicine such as, for giving MRIs, and they can be used in other fields of medicine as well, so they're very, very important, for that aspect. But radioactive isotopes can also be used for what's known as radiometric dating of fossils, and this is basically how scientists can determine how old dinosaur bones are, by just looking at the amount of radioactive isotopes that are present in the fossils and then using the half-life to calculate or approximate approximately how old the fossils are. Now we're not going to talk about that exact process but you should be aware in your biology course that radioactive isotopes will break down over time. They can have a half-life which is the time it takes for half of it to break down, and they can be used in medicine and for radiometric dating of fossils. And so this here concludes our lesson on radioactive isotopes, and we'll be able to get a little bit of practice in our next few videos.

So I'll see you all there.

Radioactive isotopes are utilized for all of the following except:

• A. Dating fossilized material of once living things.
• B. Radiation treatment to slow or stop the development of cancer cells.
• C. Labeling regions of the body with radioactivity for special imaging techniques.
• D. All of the above.

The isotope Carbon-14 has a half-life of 5,730 years. How many years must pass for a sample of Carbon-14 to break down to ¼ of its original amount?

• A. 5,730 years
• B. 17,190
• C. 11,460
• D. 2,865

Here’s what students ask on this topic:

What are isotopes and how do they differ from each other?

Isotopes are atoms of the same element that have the same number of protons but different numbers of neutrons. This difference in neutron count leads to varying mass numbers among isotopes. For example, carbon has three isotopes: carbon-12, carbon-13, and carbon-14, with mass numbers of 12, 13, and 14, respectively. Despite these differences in mass number, all isotopes of an element share the same atomic number, which is the number of protons. This is because changing the number of protons would change the element itself.

What is the significance of the atomic mass of an element?

The atomic mass of an element is the weighted average mass of all its isotopes, taking into account their relative abundances. It is different from the mass number, which is the total number of protons and neutrons in a specific isotope. For example, the atomic mass of carbon is approximately 12.011, which is close to the mass number of carbon-12, the most abundant isotope. The slight difference accounts for the presence of heavier isotopes like carbon-13 and carbon-14.

What are radioactive isotopes and how are they used?

Radioactive isotopes are unstable isotopes that decay over time, emitting energy in the form of rays or particles. This decay process is measured by the half-life, the time it takes for half of the radioactive atoms in a sample to break down. Radioactive isotopes have several important applications, including in medicine for diagnostic imaging (e.g., MRIs) and in radiometric dating to determine the age of fossils. For instance, carbon-14 is used to date ancient biological materials.

How do you calculate the mass number of an isotope?

The mass number of an isotope is calculated by summing the number of protons and neutrons in its nucleus. For example, to find the mass number of carbon-14, you add its 6 protons to its 8 neutrons, resulting in a mass number of 14. The formula can be expressed as:

$\mathrm{Mass} \mathrm{number}=\mathrm{Number} \mathrm{of} \mathrm{protons}+\mathrm{Number} \mathrm{of} \mathrm{neutrons}$

What is the half-life of a radioactive isotope?

The half-life of a radioactive isotope is the time required for half of the radioactive atoms in a sample to decay. This rate of decay is consistent and can be used to determine the age of materials, such as fossils, through radiometric dating. For example, carbon-14 has a half-life of about 5,730 years, which allows scientists to estimate the age of ancient biological materials by measuring the remaining carbon-14 content.