Isotopes - Online Tutor, Practice Problems & Exam Prep

Isotopes are atoms of the same element with the same number of protons but differing numbers of neutrons, leading to different mass numbers. 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. The half-life is the time required for half of a radioactive sample to decay, which is useful in applications like radiometric dating and medical imaging.

Isotopes

Alright, so now that we've covered the basics of the atom, in this video we're going to introduce isotopes and so all atoms of the same element are going to have the same number of protons and that's because if you change the number of protons then by definition you're going to change the element. And so 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. And this is exactly what leads us to this idea of isotopes. And so isotopes are defined as atoms of the same element that only vary in the number of neutrons and so isotopes are always, once again, going to have the same atomic numbers, and that means that they're gonna have the same number of protons. And once again, that's because if you change the atomic number or the number of protons, you're going to change the element. And so all isotopes will have the same number, same atomic number, or the same number of protons. But once again, they do not have the same number of neutrons. So that means that they will have different mass numbers, which we're called the mass number is the total number of protons and neutrons. And the reason they have different mass numbers is because they have different neutrons. And so if you have varying number of neutrons then you're automatically going to vary in the mass number. Now recall from our previous lesson, videos that not only did we define atomic number and mass number, but we also defined the atomic mass which is very similar to the mass number but it's different in the fact that it is going to be the average mass of all of the isotopes that exist for a particular, element. And so let's take a look at our example down below to look at the atomic mass of carbon's 3 isotopes.

And so you can see that we're showing you the three isotopes of the carbon atom down below. The first one is here, the second one is here, and the third one is right here. Now one thing to note about these three isotopes of carbon is that they all have the same exact number of protons. They all have 6 protons, and that is once again going to be the atomic number. So they all have the same atomic number and the same number of protons as we indicated up above. Now also notice that all three of these scenarios right here also have the same exact number of electrons. The electrons also do not vary between these three scenarios, And so, really, the only thing that differs between these three scenarios is going to be the total number of neutrons, which we have here in the middle. Notice that when you count up the number of neutrons in the nucleus of this first one there are a total of 6 neutrons, when you count up the neutrons here there are a total of 7 neutrons. And when you count up the neutrons here, there are a total of 8 neutrons. And so once again, these three scenarios right here only differ from each other in the total number of neutrons in the nucleus, and that is what makes them isotopes, atoms of the same element that only vary in the number of neutrons.

Now if we wanted to calculate the mass number for each of these three scenarios, then we need to total up the total number of protons and the total number of neutrons. But once again, the total number of neutrons is going to vary, which means that the mass number will also vary for each of these isotopes. So, if we want to determine the mass number for this first atom, we take the total number of protons, which is 6, and add that to the total number of neutrons, which is also 6, and that gives us a mass number of 12. And so this is referred to as a carbon 12 atom, and once again, it can be abbreviated as this C_126 where the 12 indicates the mass number and the 6 indicates the atomic number or the number of protons, which does not change in all of these scenarios. Now if we want to calculate the mass number of the second isotope, once again, take total number of protons, add the number of neutrons, so 6 plus 7, that gives us 13. So this isotope here is carbon 13. And so, once again, we can put the 13 up above right here to indicate its mass number. And then, if we wanted to do the same and calculate the mass number for this last, isotope over here, all we need to do is sum up the total number of protons, which is 6, plus the number of neutrons which is 8, 6 +8 is 14. So this is a carbon 14 atom.

And so, what you'll also notice is that these three isotopes can also differ in the abundance. And so, notice that this first isotope over here makes up the vast majority of all carbon atoms. In fact, it makes up about 99% of all carbon atoms, and only a small portion of all carbon atoms are made up of these other isotopes. In fact, only 1% of all carbon atoms are made up of these other 2 isotopes. And so the mass of these other isotopes, is going to have a very small impact on the average mass of all of the isotopes. And remember, the average mass of all of the isotopes is going to be the atomic mass, which is different than the mass numbers that we just calculated here. These numbers that you see here are the mass numbers and the atomic mass is once again going to be the average mass of all of the isotopes. So the atomic mass, we are showing you over here. Considering a 100% of these carbon atoms, we have to take the average. And once again, because 99% of all of the carbon atoms are carbon 12, the average is gonna be really, really close to, the mass number of the most abundant isotope. And so that's why it's 12.011. The 0.011 is coming from the small tiny percentage of isotopes that are slightly heavier than 12. And so 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.

• 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.  

• 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.

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

Radioactive Isotopes

So now that we've introduced isotopes in our previous lesson videos, in this video we're going to introduce radioactive isotopes. Radioactive isotopes are essentially isotopes that are very unstable and will eventually break down and emit energy in the form of rays or particles. If we take a look at our image on the left-hand side, you'll notice we're showing the radioactivity of a carbon-14 isotope. This represents the nucleus of the carbon-14 atom, and what you'll notice is that it has 6 protons, shown here in red, and 8 neutrons. We discussed the Carbon-14 isotope in some of our previous lesson videos, so that should be a bit familiar. This gives the Carbon-14 isotope a mass number of 14, which is why it's called Carbon-14. Once again, Carbon-14 is a radioactive isotope, so it is unstable and will break down, emitting energy in the form of rays or particles. This arrow here represents released energy, and this other arrow represents released subatomic particles. This process will break down and decay over time.

The rate at which radioactive atoms decay over time is quite consistent, and from this consistency, scientists can determine what's known as a half-life. The half-life is the exact amount of time it takes for half of all the radioactive atoms in a sample to break down and decay. From this half-life, scientists can use it for meaningful purposes, such as in medicine and for radiometric dating of fossils. You'll notice here in our image on the right-hand side, we're showing a person getting an MRI, which uses radioactive isotopes, and some fossils; the radiometric dating of these fossils relies on isotopes.

This concludes our brief introduction to radioactive isotopes, and we'll be able to get some practice applying these concepts as we move forward. So I'll see you in our next video.

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.

• 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

• 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 different mass numbers for each isotope. For example, carbon has three isotopes: carbon-12, carbon-13, and carbon-14, with mass numbers of 12, 13, and 14, respectively. Despite having different mass numbers, all isotopes of an element share the same chemical properties because they have the same number of protons and electrons. The varying neutron count, however, can affect the physical properties, such as stability and atomic mass.

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 deviation accounts for the presence of other isotopes like carbon-13 and carbon-14. Atomic mass is crucial for calculating the molar mass of compounds and for understanding the element's behavior in chemical reactions.

How are radioactive isotopes used in medicine?

Radioactive isotopes are used in medicine for both diagnostic and therapeutic purposes. In diagnostics, isotopes like Technetium-99m are used in imaging techniques such as MRI and PET scans to visualize internal organs and detect abnormalities. In therapy, isotopes like Iodine-131 are used to treat conditions such as hyperthyroidism and certain types of cancer by targeting and destroying diseased cells. The predictable decay rates of these isotopes allow for precise control over the dosage and timing of treatments, making them invaluable tools in modern medicine.

What is a half-life and how is it used in radiometric dating?

A half-life is the time required for half of the radioactive atoms in a sample to decay. This consistent rate of decay allows scientists to use half-lives for radiometric dating, a method for determining the age of fossils and geological samples. By measuring the remaining amount of a radioactive isotope and comparing it to its known half-life, scientists can calculate the time elapsed since the sample formed. For example, carbon-14 dating is used to date organic materials up to about 50,000 years old, providing valuable insights into historical and prehistorical events.

What are the three isotopes of carbon and how do they differ?

The three isotopes of carbon are carbon-12, carbon-13, and carbon-14. They all have 6 protons but differ in their number of neutrons: carbon-12 has 6 neutrons, carbon-13 has 7 neutrons, and carbon-14 has 8 neutrons. This difference in neutron count results in different mass numbers: 12, 13, and 14, respectively. Carbon-12 is the most abundant isotope, making up about 99% of all carbon atoms. Carbon-13 is stable but less abundant, while carbon-14 is radioactive and used in radiometric dating due to its predictable decay over time.