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, highlighting their significance in both scientific research and practical uses.

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, and that's because if you change the number of protons, by definition, 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, 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, and so isotopes always have the same atomic numbers, meaning they're going to have the same number of protons. If you change the atomic number or the number of protons, you're going to change the element, so all isotopes will have the same atomic number, or the same number of protons. But once again, they do not have the same number of neutrons. This means that they will have different mass numbers, which is called the total number of protons and neutrons. The reason they have different mass numbers is because they have different neutrons. If you have varying numbers of neutrons, then you're automatically going to vary in the mass number.

Now recall from our previous lessons 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 different in that it is the average mass of all of 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. You can see that we're showing you the 3 isotopes of the carbon atom here. One thing to note about these 3 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. They all have the same atomic number and the same number of protons. Also notice that all three of these scenarios also have the same exact number of electrons. The electrons also do not vary between these scenarios, so really, the only thing that differs between these scenarios is going to be the total number of neutrons, shown here in the middle. Notice that when you count the number of neutrons in the nucleus of the first isotope, there are a total of 6 neutrons, in the second there are 7 neutrons, and in the third, there are 8 neutrons. These three scenarios 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.

To calculate the mass number for each of these scenarios, we need to total the number of protons and neutrons. The total number of neutrons varies, which means that the mass number will also vary for each of these isotopes. To determine the mass number for the first isotope, we take the total number of protons, which is 6, and add that to the total number of neutrons, which is also 6, giving a mass number of 12. This is referred to as a carbon12 atom. For the second isotope, the total number is 13, which can be indicated carbon13, and the third sums to 14, indicated as carbon14 atom.

Notice that the first isotope makes up about 99% of all carbon atoms, while the other isotopes make up only 1%. The mass of these isotopes has a very small impact on the average mass of all of the isotopes, known as the atomic mass, which differs from the mass numbers we calculated. Here, considering 100% of these carbon atoms, we take the average, which is very close to the mass number of the most abundant isotope, hence it's 12.011. The 0.011 comes from the small percentage of isotopes that are slightly heavier than 12.

This concludes our introduction to isotopes, and we'll be able to get some practice as we move along through our course. 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

Alright, so now that we've introduced isotopes in this video, we're going to talk a little bit about radioactive isotopes. Radioactive isotopes are defined as isotopes that are unstable and break down over periods of time by emitting energy in the form of rays or particles. If we take a look at our image below on the left-hand side, notice that we are showing you an example of the radioactivity of a carbon-14 isotope. 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 and 8 neutrons in its nucleus since its mass number is 14. Carbon-14 is a radioactive isotope, meaning that it is unstable and will break down over time by emitting energy in the form of rays or particles. This arrow right here represents released energy, and this arrow down here represents released subatomic particles. Once again, this radioactive atom is going to decay and break down over time. The rate that radioactive atoms break down is pretty consistent, and from that consistency, scientists can calculate what is known as the half-life, which is the exact amount of time it takes for exactly half of all radioactive atoms in a sample to break down. These radioactive isotopes have several important uses in human life. 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. But radioactive isotopes can also be used for what is known as radiometric dating of fossils. 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 how old the fossils are. 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. 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.

• 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 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. The varying number of neutrons in isotopes results in different physical properties, such as stability and atomic mass.

What is the significance of radioactive isotopes in scientific research and practical applications?

Radioactive isotopes are significant in both scientific research and practical applications due to their instability and ability to decay over time, emitting energy and particles. This decay process is measured by the half-life, which is the time it takes for half of the radioactive atoms in a sample to break down. In medicine, radioactive isotopes are used in diagnostic imaging techniques like MRIs and in treatments for certain diseases. In geology and archaeology, they are used for radiometric dating, which helps determine the age of fossils and rocks by measuring the remaining radioactive isotopes and calculating their half-lives. This makes radioactive isotopes invaluable tools in various fields.

How is the atomic mass of an element calculated considering its isotopes?

The atomic mass of an element is calculated as the weighted average of the masses of all its isotopes, taking into account their relative abundances. For example, carbon has three isotopes: carbon-12, carbon-13, and carbon-14. Carbon-12 is the most abundant, making up about 99% of all carbon atoms. The atomic mass is close to the mass number of the most abundant isotope but slightly adjusted to account for the presence of the other isotopes. The formula for calculating atomic mass is:

$\mathrm{Atomic} \mathrm{mass}=\sum _{i=1}^n(\mathrm{fractional} \mathrm{abundance} \mathrm{of} \mathrm{isotope} i) \times \mathrm{mass} \mathrm{of} \mathrm{isotope} i$

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 to date materials, a process known as radiometric dating. By measuring the remaining amount of a radioactive isotope in a sample and knowing its half-life, scientists can calculate the age of the sample. For example, carbon-14, with a half-life of about 5,730 years, is commonly used to date organic materials like fossils. The formula for calculating the age of a sample using half-life is:

$\mathrm{Age}=\mathrm{half-life} \times (\log (\mathrm{initial} \mathrm{amount}/\mathrm{remaining} \mathrm{amount})/\log (2\left)\right)$

How do isotopes affect the atomic mass of an element?

Isotopes affect the atomic mass of an element by contributing to the weighted average of the masses of all the isotopes of that element. Since isotopes have different numbers of neutrons, they have different mass numbers. The atomic mass is calculated by averaging these mass numbers, weighted by their relative abundances. For example, carbon's atomic mass is approximately 12.011 because carbon-12 is the most abundant isotope, making up about 99% of all carbon atoms, while carbon-13 and carbon-14 are much less abundant. This weighted average ensures that the atomic mass reflects the natural distribution of an element's isotopes.