In this video, we'll look at an example involving trends in ionization energies. Our problem reads: "Put the elements sodium, magnesium, and silicon in order of increasing first ionization energy, second ionization energy, and third ionization energy." Our general trend from the periodic table is that ionization energies increase going up and to the right. We also have to determine whether we are removing core electrons or valence electrons. To do this, we need to write the electron configurations. So, we'll start by writing the electron configurations for sodium, magnesium, and silicon. The core electrons in these electron configurations are shown in red, and the valence electrons are shown in black. For the first ionization energy, we are removing valence electrons from sodium, magnesium, and silicon. So we can apply our trend from the periodic table that for the first ionization energy, our ionization energy will increase going up into the right in the periodic table. Therefore, our increasing order of ionization energy is sodium, magnesium, and then silicon. For the second ionization energy, we have to write the electron configurations for the ions that we're removing an electron from. After we've removed an electron, we have Na+, Mg+, and Si+. Based on these electron configurations for the second ionization energy, we're going to be removing a core electron from sodium, 10 valence electrons from magnesium, and silicon. It requires a lot more energy to remove a core electron than a valence electron. So, now for our order of increasing ionization energy, our order will be magnesium, silicon, and then sodium. Because we're removing a core electron from sodium, it requires significantly more energy than removing valence electrons from magnesium and silicon. For our third ionization energy, we need to start by writing the electron configurations for the ions from which we're removing the third electron. So, we will be removing an electron from Na2+, Mg2+, and Si2+. Now, we are removing core electrons from both sodium and magnesium, and we'll be removing a valence electron from silicon. Therefore, our order of increasing third ionization energy becomes silicon, then sodium and magnesium. Silicon has the lowest third ionization energy because it's removing a valence electron. And when comparing removing an electron from sodium and magnesium, because we're removing core electrons from both, it follows our pattern again of increasing going up into the right in the periodic table.