### Video Transcript

The diagram shows electrons in different electron shells in an atom. The atom is electrically charged and has one less electron in its outer shell than it would if it were electrically neutral. What element is this an atom of?

The question has given us this diagram, which we’re told shows an atom with electrons in different electron shells. This red circle here at the center represents the nucleus of the atom, and this is where all of the atoms, protons, and neutrons are found. Then around this nucleus, we can notice that there are these three black rings that have small blue circles drawn on them. These rings represent the atom’s first three electron shells, which are shells where the atoms electrons can be found. The shell that’s closest to the nucleus is known as the atom’s first electron shell. Then, the next shell out is the second electron shell. And then out from this, we have the third electron shell.

Each one of these small blue circles that’s drawn on each of the three rings represents an electron that’s in the corresponding electron shell. The question is asking us to identify what element this is an atom of. We can recall that the element of an atom is determined by that atom’s atomic number and that atomic number is equal to the number of protons in the atom’s nucleus. So then to work out what element this is an atom of, we need to work out how many protons there are in this nucleus.

In the diagram that we’re given, the individual protons and neutrons within the nucleus aren’t shown. Instead, the nucleus is just drawn as a single red circle. This means that we can’t count the atom’s protons directly, and instead, we’ll need to find another approach. Now we might not be shown all of the individual protons, but in this diagram, we clearly are shown all of the atom’s individual electrons.

The question tells us that this atom has one less electron in its outer shell than it would do if it were electrically neutral. An atom that’s electrically neutral is an atom that has no overall electrical charge. Let’s recall that protons and electrons are both electrically charged particles. In fact, we can further recall that the electron charge and the proton charge are equal in magnitude but opposite in sign. Protons are positively charged, while electrons are negatively charged. So in order for an atom to be electrically neutral, the number of negatively charged electrons would have to be equal to the number of positively charged protons. In that case, all the negative charges and the positive charges would exactly cancel out, leaving no overall electrical charge.

However, that’s not the case for the atom in this question which we’re told is electrically charged. Specifically, we know that in the outer shell of this atom there’s one less electron than there would be if the atom were electrically neutral. In other words, then for this atom, the number of electrons that it has is equal to the number of protons minus one. That’s because the number of protons in the atom is equal to the number of electrons that it would have if it were electrically neutral. And we’re told that it’s got one less electron than that. So, we subtract one.

In this equation, we’re trying to find the number of protons because we know that this is equal to the atom’s atomic number. With that in mind, let’s clear some space on the board so we can rearrange the equation to make the number of protons the subject. We have shown that for the atom in this question, the number of electrons, which we’ve written here as 𝑁 subscript e, is equal to the number of protons, which we’ve labeled as 𝑁 subscript p minus one. In order to make the number of protons 𝑁 subscript p the subject, we want to add one to both sides of the equation because then on the right-hand side, the minus one and the plus one cancel each other out.

If we then write the equation the other way around, we have that the number of protons 𝑁 subscript p is equal to the number of electrons 𝑁 subscript e plus one. This equation means that if we can count up the number of electrons in this atom, we can use that number to find the number of protons to find the number of electrons. We just need to count up the number of small blue circles that are drawn on each of the three rings in the diagram.

On the innermost ring, which represents the first electron shell, we find that there are two electrons in total. Then for the next ring out from this, which represents the atom second electron shell, when we count up all of the small blue circles that are drawn on this ring, we find that in total there are eight of them. So, this means that there are eight electrons in the atom second electron shell. Lastly, on the third ring representing the third electron shell, there’s just one blue circle, so there’s one electron in the third shell.

So, this atom has two electrons in the first shell, eight electrons in the second shell, and one electron in the third shell. This means that the total number of electrons in the atom, 𝑁 subscript e, is equal to the two from the first electron shell plus the eight from the second electron shell plus the one from the third shell. This works out as a total of 11 electrons. If we now substitute this value for 𝑁 subscript e into this equation, we find that 𝑁 subscript p, the number of protons, is equal to 11 plus one, which works out as a total of 12.

Since we know that the number of protons in an atom is equal to that atom’s atomic number, then we know that this atom has an atomic number of 12. At this point, we can either recall or look up in a periodic table that the element with atomic number 12 is magnesium. So, our answer to this question is that the atom that’s shown in the diagram is an atom of the element magnesium.