Isotope A decays to isotope E through the following series of steps, in which the products of the individual decay events are themselves radioactive and undergo further decay until a stable nucleus is ultimately reached. Two kinds of processes are represented, one by the shorter arrows pointing right and the other by the longer arrows pointing left. (b) Identify and write the symbol for each isotope in the series:

Video transcript

Hey everyone, we're asked to consider isotope one which undergoes radioactive decay to produce another radioactive new glide that undergoes another radioactive decay until isotope five is produced. There are two types of decay processes, One depicted by shorter arrows pointing to the right and the other depicted by longer arrows pointing to the left, determine the identity of each species in the series by providing their isotopic symbol. So first, let's go ahead and start with isotope one. Now, for isotope one, we can see that we have neutrons And we can see that we have an atomic number of 90. Now, when we look at our periodic table, we see that our element comes up to be thorium. Now all we need to do is determine our mass number, which is our A. In order to determine our a. We just need to take our number of neutrons and add the number of protons, which gets us to a mass number of 2:31. So our final symbol is going to have to 31 at the top left and a 90 on our bottom left. Now, let's go ahead and look at isotope too. For Isotope two, we can see that we have 140 neutrons and we have an atomic number of 91. So this means we have protected me um as our element now to determine our mass number, we're going to take 1 40 plus 91 which gets us to a mass number of 2 31. And this will be our final isotopic symbol. Now let's go ahead and look at isotope three. For isotope three, we can see that we have 138 neutrons based on our graph. Looking at our atomic number, We can see that we have 89. Looking at our periodic table, we find that our element comes up to be acting ium determining our mass number. We're going to take our neutrons of 1 38 and add our protons of 89. This gets us to a mass number of 2 27. So our final isotopic symbol will be this. Now let's go ahead and look at ice tobe number four for isotope number four, we can see that we have 137 neutrons and we have an atomic number of 90. When we look at our periodic table, this comes up to be thorium. Now to determine our mass number, we're going to take 1 37 and add 90 which gets us to a mass number of 27. So we have 227 at our top left and 90 at our bottom left. And this is going to be our final isotopic symbol. Finally looking at Isotope five, we can see that we have 135 neutrons And we have an atomic number of 88. When we look at our periodic table, this tells us that our element is radium. Now to determine our mass number, we're going to take 1:35 and add 88, which gets us to a mass number of 2:23. So we have 223 at our top left, and 88 at our bottom left, and this will be our final symbol. Now, I hope this made sense and let us know if you have any questions.