The nuclear equation carbon with a mass number of 14 and an atomic number of six decaying to nitrogen with a mass number of 𝑛 and an atomic number of seven plus a 𝛽-particle with a mass number of zero and an atomic number of negative one shows how carbon decays to nitrogen via 𝛽-decay. What is the value of 𝑛 in the equation?
Okay, so in this question, we’re trying to find out the value of 𝑛, which is up here in the equation. And to do this, we need to know one important fact. The fact that we need to know is that, in a nuclear equation, the total mass number is conserved.
What does this mean? Well, what it means is that the total mass number on the left-hand side of the equation, the LHS, is equal to the total mass number on the right-hand side of the equation. In other words, the total mass number on the left, which is 14 in this case, cause all we have is the mass number of carbon, is equal to the total mass number on the right, which happens to be the mass number of nitrogen, which is 𝑛 plus the mass number of the 𝛽-particle, which is zero. So 14 is equal to 𝑛 plus zero. And therefore, we’ve already found our final answer. The value of 𝑛 is equal to 14.