Bismuth-212 attaches readily to monoclonal antibodies and is used in the treatment of various cancers. This bismuth-212 is formed after the parent isotope undergoes a decay series consisting of four α decays and one β decay (the decays could be in any order). What is the parent isotope for this decay series?

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Hey, everyone. We're told that the isotope radium 2 23 is used in bray therapy. The radiation is used to kill cancer cells and reduce tumor size. A radium 2 23 isotope is produced when a parent nu Clyde undergoes three alpha decays and two beta decays. Not necessarily in any particular order, give the identity of the parent nu glide in the decay series. First, let's go ahead and talk about our isotopic symbol where X represents our element symbol. A represents our mass number N Z represents our atomic number. So for our product Radium 2, 23 We have our element radium and its mass number is 223. When we look at our periodic table, we find that its atomic number is 88. Now, before we identify the parent new glide, let's first discuss what happens in an alpha decay. And a beta decay starting off with an alpha decay, we have an alpha particle And the alpha particle can be written like so where we have our alpha particle and it has an a of four And a Z of two. So this would reduce mass number by four and reduce the atomic number by two. Now let's go ahead and take a look at our beta particle for our beta particle. We have our beta symbol. We have a 04 mass number and a negative one for our atomic number. In this case, this does not change our mass number, but it increases atomic number by one. Now that we've written this out, let's go ahead and identify our parent new glide. So we have our radium 223 And we're first going to add those three alpha decays. So we have three and here we will input our alpha particle and we're going to add two of our beta particle. Now, let's go ahead and solve for apparent new glide Starting off with a which is our mass number. We have 223 from our radium and we're going to add three Times four From Our Alpha Particle. And we're also going to add two times zero from our beta particle Solving for a. We end up with an a of 2:35. Now, let's go ahead and take a look at our Z For our Z. We have 88 from our radium And we're going to add three Times two From Our Alpha Particle. And we're also going to add two times negative one from our beta particle Solving for Z, we end up with a Z of 92, which is our atomic number. Now, when we look at our periodic table we find that uranium Has the atomic number of 92. So rewriting this in its isotopic symbol, we have our uranium, which symbol is you A mass number of And an atomic number of 92. And this will be our parent new glide. Now, I hope this made sense and let us know if you have any questions.

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Key Concepts

Decay Series

Alpha Decay

Beta Decay