Write balanced nuclear equations for the following processes:

(a) rubidium-90 undergoes beta emission.

Video transcript

All right. Hello everyone. So this question is asking us to write down the balanced nuclear equation for the beta emission of barium 138. And here we have four different entry choices labeled A through D. So lets go ahead and quickly recall how to go ahead and write general isotope notation. So first, we're going to have an elemental symbol which I'm going to call X. In this general example, to the left of the element symbol are going to be two numbers. The superscript on the top is going to be represented as a, which represents the mass number of that particular isotope. And so the subscript, in other words, the number on the bottom here, which I'll call Z is the atomic number of that element. So in this particular case, we're going to represent the beta emission of barium 138 which means that barium 138 is going to be the reactant here. The symbol for barium is B A and the superscript is going to be 138 since that's the mess and barium has an atomic number of 56. So that's going to be the subscript here. So now barium 138 is going to undergo beta emission. So here our product is going to be or products I should say are one daughter nuclei which will identify in a moment and the beta particle itself. Now the beta particle is represented as the symbol E with a mass of zero and negative one as the atomic number or in other words, the subscript to the left of the symbol. So in this case, we're going to go ahead and identify the daughter nuclei by balancing out both sides of the equation. And so what that means is that the values for both A and Z must be equal to each other on both sides of the arrow. So let's go ahead and balance out a first on the left side, A is equal to 138. And on the right side, the sum of the mass numbers of both products here should equal 138. So that's 138 is equal to a added to zero. This means that A which is the mass of the daughter nuclei here should also be 138. So I'm going to substitute that in my equation here. So now let's go ahead and balance out the atomic numbers or the subscripts here. So to balance out the on the left side, we have 56 and 56 should be equal to the sum of Z and negative one. So now because of that negative number, what that does is actually add 1 to 56 which means that Z of the daughter nuclei is equal to 57. And now that we know that the atomic number of the daughter nuclei is 57 we can identify that in the periodic table as lanthanum. So I am going to replace X with the symbol for lanthanum thats L A and there you have it. And so the balance reaction is as follows. We have barium 138 with an atomic number of 56 producing lanthanum 138 with an atomic number of 57. And that beta particle, this corresponds to option B in the multiple choice. And so with that being said, thank you so very much for watching. And I hope you found this helpful.