Write balanced nuclear equations for the following transformations:

(b) nitrogen-13 undergoes electron capture.

Video transcript

All right. Hello everyone. So this question is asking us to give the balanced nuclear equation for the electron capture process of silver. 102. Here we have four different entry choices labeled a through D proposing different possible equations. So first, let's clarify a few things about general isotope notation. Before proceeding with the actual equation, let's say that I have a generic element with an atomic symbol of X to the left of the symbol are going to be two numbers. We have a superscript on the top and a subscript on the bottom. Now, the superscript should represent the atomic mass of the element or the isotope I should say which I'm going to abbreviate as a here. On the other hand, the subscript on the bottom represents the atomic number of that element which is abbreviated here as Z. So A stands for the atomic mass and Z stands for the atomic number. So now lets talk about our reactant which is silver, 102 silver has a symbol of A G and silver has an atomic number of 47 meaning that 47 should be the subscript on the bottom here. Now, the mass of this particular isotope is 102. So that's going to be the superscript. However, in addition to silver 102 recall that during an electron capture process, the electron that's being captured is also going to be a reactant on the left side of the equation. So our second reactant is going to be that electron that has lowercase E as its symbol, a mass number of zero. And the subscript on the bottom is going to be negative one. So from here, the identity of the product otherwise known as the daughter nucleus is going to be the result of balancing both sides of this equation. Because first, we have to figure out what the mass number and atomic number of the daughter nucleus is going to be, which we can then use to find the symbol. And the way that we find that information is by balancing out both sides of the equation like so let's start off with the atomic mass of the daughter nucleus. So here in trying to find the value for a of the daughter nucleus that is going to be equal to the sum of the mass numbers on the reacted side because the mass numbers and the atomic numbers should be balanced on both sides of the equation. In other words, 102 added to zero should equal the mass number on the right side. So after evaluating this expression, a for the daughter nucleus here is going to be 102. So now the atomic number can be found in a similar way here. 47 add it to negative one should equal to Z which represents the atomic number of the daughter nucleus. So when evaluating this Z is equal to 46. So now the daughter nucleus has a mass number of 102 and an atomic number of 46 the atomic number of 46 identifies the daughter nucleus as palladium, which has a symbol of PD and there you have it. So after the electron capture process, silver 102 became palladium 102. And that corresponds to option A in the multiple choice. And so with that being said, thank you so very much for watching and I hope you found this helpful.