 We often come across articles with these titles. Some researchers find some algae that is 541 million years old, or a cave with fossils 500,000 years older than we thought, or a fossil in the form of a million years old tooth. How do these scientists and researchers figure out the age of all of these fossils? When experts examine fossils, they use a technique that involves counting radioactive atoms, or let's call them unstable atoms, of certain elements that are still present in a sample. They do that by using an instrument called a mass spectrometer. The goal of this video is to figure out the workings of a mass spectrometer, and also how it helps in determining the age of a fossil. All right, so let's begin. Before looking into the workings of a mass spectrometer, let's look at something interesting that happens in our atmosphere and ecosystem, which plays a huge role in determining the age of fossils. So we know that every living thing is made of carbon. Plants can photosynthesize, use the carbon in the atmosphere to make sugars, and animals, including us, can eat these plants, and that's how the carbon enters our body. But it turns out that there is more than one form of carbon. There are different versions of the element carbon. Most carbon atoms have six protons and six neutrons, and this is carbon 12, and it is written like this. You have 12, the total number of protons and neutrons, and six protons, and here is your carbon symbol. But some have six protons and eight neutrons, and this is carbon 14, because now the total number of nucleons or the mass number is 6 plus 8, that is 14, and this is carbon 14. These two are versions of the element carbon, with carbon 12 present in the highest amount, and some of the carbon atoms are also carbon 14 atoms that are present in the atmosphere. For human or animal remains from the past 50,000 or 60,000 years, researchers look at the level of carbon 14 in the sample. Why and where does it come from? Let's look at that. Up high in the Earth's atmosphere, we know that the element that is present in the highest amount is nitrogen, and the carbon 14 isotope is produced when cosmic rays, and these could be coming from the Sun or any star, when these cosmic rays strike the nucleus of the nitrogen atom, turning it into a carbon 14 atom. And it does that by knocking off one proton, one pink dot out of nitrogen nucleus, and adding a neutron in place of it. We know that an element is defined by the number of protons that it has. So nitrogen, which had seven protons, has now become an isotope of carbon, having six protons, and carbon 14 to be particular. Now if we compare carbon 14 and carbon 12, we notice that even though they have different number of neutrons, they still have the same number of protons, which means they have the same number of electrons. So because the number of electrons are the same in these two versions of the element carbon, in carbon 12 and carbon 14, their chemical properties are more or less the same. They react with things similarly. That allows the plants to absorb it during photosynthesis and then pass it up the food chain. That is how carbon 14 enters our body. This process of nitrogen changing into carbon 14 is not something that happens every once in a while. It's a constant process happening at a steady rate. So much so that at any given point, the ratio of carbon 14 atoms and carbon 12 atoms in the air or in any plant issue or even in us remains approximately the same. This ratio turns out to be a fixed number in living organisms and even an atmosphere. The interesting bit is when the plant or the living organism dies. Now they're not taking up anything. So no entry of carbon 14. The entry of carbon 14 is frozen, but it turns out that carbon 14 is unstable or radioactive in nature. It starts decaying back to nitrogen. It starts decaying back to nitrogen. So carbon 14, it starts decaying back to nitrogen and turns out for half of carbon 14 or for 50% of carbon 14 to decay back to nitrogen, it takes around 5,730 years. So researchers compare the amount of carbon 14 with the levels of carbon 12 and sometimes carbon 13, but mostly carbon 12 to determine how much time has passed since an organism died. If this ratio came out to be half of what it should be, then it means that 50% of carbon 14 has decayed back to nitrogen and it takes 5,730 years to do that. So then we can estimate that the age of that fossil is somewhere around 5,730 years. Now comes a question of how does one even find this ratio? For that, let's go to the mass spectrometer. It has five steps and we start with the first step of ionization. The sample or the fossil is vaporized, introduced into this vacuum chamber. The sample could be in a solid form or in a gaseous form. Mostly it's in a gaseous form. It's vaporized. Now here the sample is bombarded with fast moving electrons. These electrons knock off other electrons from the atoms in the vapor and they turn into positive ions. Most of the positive ions formed will carry a charge of plus one because it is much more difficult to remove further electrons from an already positive ion and you have a mix of carbon 14 and carbon 12 positive ions in this vapor now. Now these positive ions, they have to be pushed into the other parts of the instrument. So these positive ions are then accelerated out into the rest of the machine. They are pushed and accelerated across this space of uniform electric field pointing to the right. For this we can use two plates with a potential difference of delta v and they should be having slits where the ions could come in and move out and the first plate can be at a higher potential than the second plate so that we have electric field lines pointing to the right. Now all the ions are moving to the right but they are still all moving with different velocities because that's how they started in the vapor form right with all the atoms moving at random velocities. And usually usually this is how the velocities are distributed. The y-axis represents a fraction of atoms moving with some velocity v. So let's say for example if we look at the velocity of 500 meters per second then it's possible that let's say 40% of all the atoms in this vapor they are moving with this velocity of 500 meters per second. And it also means that in that 40% x% of carbon 14 ions and y% of carbon 12 ions will be moving with this velocity. Similarly if we look at 250 meters per second maybe 30% of all the atoms are moving with this velocity. And in that 30% x% of carbon 14 and y% of carbon 12 will be moving at 250 meters per second. So it turns out that the ratio of carbon 14 to carbon 12 atoms moving with any velocity is the same. Now we could be letting all of these ions with all the velocities pass through the second stage but we won't do that. We will be picking out any one velocity, either 500, 250 or any any one velocity. And we will count the presence of carbon 14 and carbon 12 ions moving with that one velocity. Why are we doing that though? Why aren't we letting all the ions pass through this slit right here? We will see the reason for that in a while. But to get all the ions moving with any any one velocity we can use a velocity selector. As the ions enter they experience an electric force in the downward selection in this case because the top plate is positively charged and the bottom plate is negatively charged. So the electric field lines go from positive to negative. So you have the force on the ion due to the electric field in the downward selection. And magnitude of this force, magnitude of this force is q times the magnitude of electric field. For this velocity selector we have the magnetic field that is going inside the plane of the screen and we know that moving charges experience a force in a magnetic field and that force is q into v cross b. We can figure out the direction of the magnetic force on the ions using the right hand curl rule. Here we are curling our fingers from v to b. v is in the right direction and the magnetic field is inside the plane of the screen. So curling from v to b we notice that the thumb points in the upward direction and that is the direction of the force. So the force on this ion is upwards and the magnitude would be q v b. Now only if these two forces are balanced only then the ions will pass through this velocity selector. Otherwise if one force dominates then the ion will get deflected in that direction and strike the wall of the plate and not escape the velocity selector. So if the force is acting on the ions are balanced and that means that means q e q e q e should be equal to q v b and from here we can write v that is equal to e divided by b. Only for ions moving with this velocity e divided by b only those ions will pass through the velocity selector. So we have selected one velocity and all of the carbon 14 and carbon 12 ions that are moving with this one particular velocity which depends on the magnitude of electric field and the magnitude of magnetic field. Only these ions will pass through the velocity selector into the remaining parts of the mass spectrometer and the next step is again entering a region of uniform magnetic field. In this case the magnetic field is pointing outside the plane of the screen. The direction could be inside or outside that doesn't really matter but for this case we can assume that the magnetic field is pointing outside the plane of the screen and it's also a uniform magnetic field. Now as these ions enter this region of magnetic field we know that they will experience a force because moving charges experiences a force in a magnetic field and the direction of the force can again be figured out using the right hand curl rule. In this case again we are curling our fingers from v to b from v to b. v is to the right and b is outside the plane and we notice that the thumb is pointing downwards so that is the direction of that is the direction of the force. So as the carbon 12 and carbon 14 ions enter both of them experience a force in the downwards direction. We also see that the force is perpendicular to the direction of velocity and that is true for the entire duration that the charge is moving inside this region of uniform magnetic field. So as the charge enters it experiences a force downwards so it's so it deflects slightly but the force is still perpendicular to the direction of its velocity. So as a result of this the path that the ion traces looks looks like this. Let me make this slightly transparent so that we can see the path clearly there you go. The ion traces a semicircular path and we can figure out the radius of this path using the idea that the magnetic force or the Lorentz force is acting as the centripetal force for this ion. So when we do that we can write q v b which is this is equal to m v square divided by r and on solving this we get the radius as m v divided by q b. Now we can look at this relation closely. We know that q b that is constant this is a uniform magnetic field of known value and the charge is just positive one in this case and we know the velocity with which the charge is also moving because we just filtered all the other velocities and we are we only took one velocity we selected one velocity using the velocity selector. So the radius of the semicircular path only depends on the mass of that ion. The heavier the mass if the mass of that ion is more it will create a semicircle with a larger radius. So between carbon 12 and carbon 14 we know that carbon 14 has a higher mass number 14 so it has a higher atomic mass so carbon 14 should trace a semicircle with a larger radius and carbon 12 ion will also trace a semicircular path but the radius of that semicircle will be smaller than that of carbon 14 because the mass of carbon 12 ion is less than the mass of carbon 14 ion and the radius is only dependent on mass and that is that is the use of velocity selector here because v is constant q we know is constant b is constant so we get a very simple direct relation of the radius and the mass. Now finally what happens what happens when they when they finish making the semicircle let me make some space for that finally these ions strike the detector which transfers a small amount of current from the positions where the ions strike using this relation we know where carbon 12 and carbon 14 will strike because from the entry point this distance is just two hours for both and the amount of current coming out from these positions gives us some idea into the number of the number of ions striking these positions the small amount of current is then amplified and that helps us generate a mass spectrograph this is called a mass spectrograph this tells us the relative abundance or or the amount of different atoms in the sample this would be in percentage but from here we can get an idea of the ratio of carbon 14 atoms to carbon 12 atoms in this sample and comparing this ratio with the original ratio of carbon 14 to carbon 12 in living organisms we can get an idea of how much carbon 14 has decayed and thus how old the fossil is because we know that when 50 percent of carbon 14 is decayed it takes 5,730 years so if this ratio came out to be half of c14 to c12 in living organisms then the fossil is 5,730 years if this ratio came out to be one by fourth then the fossil would be approximately 11,000 years old you will learn more about how atoms decay turns out they don't decay linearly they follow an exponential form you will learn more about that in other Khan Academy videos but the main thing here is the working principle of the mass spectrometer that is separating ions on the basis of their mass so that we get an idea of how many ions are present in the sample there are some limitations to measuring the ratio of carbon 14 to carbon 12 one of them is that since it only takes 5,730 years for 50 percent of carbon 14 to decay samples that are older than let's say around 40,000 years are extremely difficult to date due to tiny levels of carbon 14 also the ratio of carbon 14 to carbon 12 is something that is changing now in the atmosphere because of our industrial activities in spite of these limitations and challenges researchers still use this decay of carbon 14 as a kind of atomic clock which helps them look into the past and figure out the date of dead animals plants and other kind of carbon based fossils