in this lesson we're going to talk about how to calculate the number of protons neutrons and electrons in an atom and in an ion so let's use sodium as an example and on a periodic table you might see something that looks like this the smaller of the two numbers is the atomic number which is also equal to the number of protons the larger of the two numbers is known as the average atomic mass now sometimes you might see a problem that's written this way they may tell you to find the number of protons neutrons and electrons for this particular element now in this format you can see that the atomic number is on the bottom the number on the top notice that it's not the same as 22.99 in fact it's rounded this is not the average atomic mass but rather it is the mass number so this is a specific isotope of sodium if you average all of the isotopes of sodium on earth you're going to get this number so because that number is close to 23 this is the most abundant isotope of sodium on the earth so in addition to sodium 23 you also have sodium 24 and there's also sodium 22. but as we said before because the average atomic mass was 22.99 this is the most abundant isotope which is also the most stable one on the earth the other forms of sodium they're not stable and they're not very common but these are other isotopes of sodium now what you need to know is that the atomic number is associated with the identity of the element so sodium always has an atomic number of 11. now the mass number can change and it will change for different isotopes so that number can vary but the identity of the element is dependent on the atomic number now let's talk about the formulas that we need in order to calculate the number of protons neutrons and electrons so let's start with the number of protons this is always equal to the atomic number that's it so sodium always has 11 protons now the number of neutrons is the difference between the mass number and the atomic number and then the number of electrons is equal to the atomic number minus the charge of the species so for an atom let's say like aluminum which doesn't have a charge the charge is zero the electrons will thus be equal to the atomic number so for an atom the number of electrons and protons are the same because the atom is neutral but if we have an ion let's say a positively charged cation then the number of electrons will change in this case there's going to be three more protons than electrons or if we have an anion like the phosphide anion there's going to be three more electrons than protons so for ions the number of electrons and protons are different but for atoms which are electrically neutral the number of protons and electrons are the same so let's start with this example go ahead and calculate the number of protons electrons and neutrons for this element so the number of protons is equal to the atomic number which is the smaller of the two values so that's going to be 11. the number of neutrons is the difference between the mass number which is 23 and the atomic number which is 11. so it's 23 minus 11 and that gives us 12. so we have 11 protons 12 neutrons now for the number of electrons it's equal to the atomic number which is 11 minus the charge now there's no charge for this particular element it's an atom not an ion so the charge is zero so we have 11 electrons so as we can see for electrically neutral atoms the number of protons and electrons are the same now let's consider another example aluminum 27 with a three plus charge so here we have an ion go ahead and calculate the number of protons neutrons and electrons in this ion so we can see that the atomic number is 13 and the mass number is 27 so the number of protons is always equal to the atomic number which is 13 in this example now the number of neutrons is the difference between the mass number and the atomic number so it's 27 minus 13 which gives us 14. now for the number of electrons it's going to be the atomic number which is 13 minus the charge on the ion which is positive 3. so 13 minus 3 is 10 so for positively charged cations there's going to be more protons than electrons so because it has a positive three charge there's three more protons and then electrons now let's try a negatively charged anion so this is the sulfide ion and let's calculate the number of protons neutrons and electrons so we have an atomic number of 16 and a mass number of 33. so the number of protons just like before is equal to the atomic number so that's 16. the number of neutrons is a difference between the mass number and atomic number so 33 minus 16 so we have 17 for this example and finally the number of electrons is the atomic number which is 16 minus the charge which is negative two so 16 minus negative two is the same as 16 plus two so we get 18 electrons thus for negatively charged ions or anions you're going to have more electrons than protons for an ion with a negative two charge there's two more electrons than protons now let's try a different example or at least one that's presented in a different way find the number of protons neutrons and electrons in silicon 29 so in this example we need to write this in a format that we're familiar with so silicon 29 that tells us that the mass number is 29 but what about the atomic number well we need to use the periodic table so if you go to it if you don't have one you can go to google images you'll find that silicon is the 14th element in the table so it has an atomic number of 14. now there was no charge indicated in this problem so we're going to assume that we're dealing with an atom and not an ion thus we have 14 protons because that's the atomic number and the number of neutrons is going to be the mass number minus the atomic number so that's 29 minus 14 which gives us 15. finally the number of electrons is going to be the atomic number minus the charge so it's 14. so for all atoms the number of protons and electrons are the same now let's work on a challenge problem so let's see if you truly understand the lesson in this video so we have a cation with a four plus charge and it has 26 neutrons and 18 electrons what is the identity of the element feel free to pause the video if you want to try it by the way for those of you who haven't done so already feel free to subscribe to this channel and don't forget to click on that notification bell and now let's begin working on this problem so right now we're going to say that the unknown element is element x so we know it has a four plus charge and the number of neutrons is 26 the number of electrons is 18. in order to determine the identity of the element what do we need to know remember the atomic number identifies the element so if we can determine the number of protons we can identify the unknown element and so that's what we need to do in this example now which of the three formulas that we wrote in the beginning can help us here is it this one the number of protons is equal to the atomic number now this is not going to help us because we know neither of these could we use this the number of neutrons is equal to the mass number minus the atomic number now we have the number of neutrons but we don't know the mass number or the atomic number so the formula that is going to be helpful is the third one the number of electrons is equal to the atomic number minus the charge because we know the charge and the number of electrons with that we can calculate the atomic number so there's 18 electrons and i'm just going to write a for atomic number and the charge is positive four so this becomes a minus four so we need to add four to both sides and so the atomic number is 22 and the number of protons is equal to the atomic number which is 22. now if we wish to calculate the mass number we can the number of neutrons was the difference between the mass number and the atomic number if you rearrange that equation you'll find that the mass number is the neutrons plus the atomic number or you could say is the neutrons plus the protons because the protons is the same as the atomic number so it's 26 plus 22 which is 48. now granted that last step wasn't really necessary but i decided to do it anyway for those of you who were curious on how to get it but let's focus on this number so if you go to the periodic table and look for element 22 let me get mine's real quick you'll find that this corresponds to titanium so this is the titanium four plus ion and this is the answer so titanium is the unknown element and that's how you can identify any unknown element for these types of problems once you identify the number of protons you could use a periodic table to identify them as an element