 Now that we are familiar with quantum numbers, let's solve a couple of questions on the same. So the first question that we have here says which set of quantum numbers describes an electron that is removed most easily from a neutral chromium atom in its ground state. This looks like a very lengthy question but it's pretty straightforward. You need to identify the last or the most ionizable electron and then figure out which set of quantum numbers describes it. So the first thing that we need to do is write down the electronic configuration of the neutral chromium atom. Atomic number of chromium is 24. And you might be tempted to write this as the electronic configuration of chromium but actually the electronic configuration is 3d5 4s1. This is because half a d orbitals offer extra stability and lowers the overall energy of the atom. Now the electron that can be most easily removed from the chromium atom would be the one that has the highest energy or the one that is present in the highest energy orbital. Now this is because the higher energy orbitals are farther away from the nucleus and therefore has less attractive pull towards the nucleus right? And that means it would be easier to knock off these electrons as compared to the lower energy orbitals which are closer to the nucleus. Now in the case of chromium the highest energy orbital would be the 4s orbital. Now this might be slightly different from what we would have normally expected but you see as we enter the transition elements that is from scandium onwards the energy of the orbitals kind of swap. For these elements the 4s orbitals are slightly higher in energy than the 3d orbitals and the electronic configuration of chromium would be 4s1 and 3d5 and that means the most ionizable electron in the neutral chromium atom would be the 4s1 electron. That means when the chromium atom undergoes ionization it would be this 4s electron that would leave first. Now the set of quantum numbers that describes the position and the behavior of an electron is given by n, l, m, l and ms quantum numbers. n which is the principal quantum number describes the energy of the electron in this particular orbital. Now the value of n for the electron in 4s orbital would be yes 4 because the electron is in the fourth shell. Now the quantum number l determines the shape of the orbital and also the amount of angular momentum an electron has. Now the electron is in the 4s orbital so the shape of this orbital is spherical that is because it is in the s orbital right and the value of l that corresponds to the s orbital is 0. Now the third quantum number is ml which is the magnetic quantum number and it tells as the number of orbitals that are present inside the sub-shell and their orientation within it. Now since ml is dependent on l and the value of l is 0 the value of ml is also 0. If the value of l was let's say 1 then the value of ml could be from minus l to plus l which means it could have minus 1, 0 and plus 1 values and these would correspond to the p orbital but what we have here is the s orbital right. So the ml value for the s orbital is 0. Now lastly the spin quantum number represented by ms can be either plus half or minus half. So basically this is the set of quantum numbers that describes the 4 is 1 electron of a neutral chromium atom. Let's look at another question. How many electrons in an atom of argon have ml value of 1? So here again we first need to write down the electronic configuration of argon. It has 18 electrons and the electronic configuration would be 1s2, 2s2, 2p6, 3s2 and 3p6. Now we already know that ml refers to the magnetic quantum number and it tells us how the various orbitals are oriented inside a sub-shell. So to figure out which electrons would have a value of ml is equal to 1 let's look at the electronic configuration and see the number of orbitals or the type of orbitals that are present in them. And here we have only s and p orbitals. Now we know that for an s sub-shell the l value is 0 and the ml value is also 0 and for a p sub-shell the l value is 1 and the ml value can range from minus l to plus l and that means it can have minus 1, 0 and plus 1 values that corresponds to the 3 different orbitals px, py and pz. So as we can see here ml which stands for magnetic quantum number tells us how the orbitals are oriented in different directions. For example the px orbital is oriented along the x axis, py along the y axis and the pz orbital is oriented along the z axis. So that means the electrons with ml is equal to 1 value should belong to the p orbital and how many p orbitals do we have? We have p orbitals at the second energy level and the third energy level. So if I draw a 2p and 3p orbital here and the ml values for these orbitals would be obviously minus 1, 0 plus 1 and minus 1, 0 plus 1 correct? And we know that every orbital can accommodate 2 electrons. And as you can see there are 2 electrons in the 2p orbital and 2 electrons in the 3p orbitals which have ml is equal to plus 1 value and that means we have a total of 4 electrons that have ml is equal to 1 value in an atom of argon.