Balancing nuclear equations is slightly different than balancing chemical equations. The major difference is that in nuclear reactions, we must account for protons, neutrons, and electrons, as well as write out the symbols for various chemical elements. In a nuclear equation, the products and reactants are symbolized as AZX, where X is the chemical symbol for the element, A is the mass number, and Z is the atomic number. There are two main rules to remember when balancing nuclear equations: 1. The total of the superscripts (mass numbers, A) in the reactants and products must be the same. 2. The total of the subscripts (atomic numbers, Z) in the reactants and products must be the same. Part A: What is the value of A in the following nuclear reaction? 230/90Th → 226/88Ra + AZX Express your answer as an integer. A = Part B: What is the value of Z in the following nuclear reaction? 230/90Th → 226/88Ra + AZX Express your answer as an integer.
The Correct Answer and Explanation is:
Part A: What is the value of A in the following nuclear reaction?
230/90Th → 226/88Ra + AZX
To balance the nuclear equation, we need to ensure that both the mass numbers (A) and atomic numbers (Z) on both sides are the same. Let’s break down the steps:
- Mass Number (A) on the Reactant Side:
- The mass number for Thorium (Th) is 230 (this is the number given in the equation: 230/90Th).
- Mass Number on the Product Side:
- The mass number for Radium (Ra) is 226 (from 226/88Ra).
Now, the total mass number on the product side must add up to 230, which is the mass number on the reactant side. We can write the equation as:
230=226+A230 = 226 + A230=226+A
To find A, we solve for it:
A=230−226=4A = 230 – 226 = 4A=230−226=4
So, A = 4.
Part B: What is the value of Z in the following nuclear reaction?
230/90Th → 226/88Ra + AZX
- Atomic Number (Z) on the Reactant Side:
- The atomic number for Thorium (Th) is 90 (from 230/90Th).
- Atomic Number on the Product Side:
- The atomic number for Radium (Ra) is 88 (from 226/88Ra).
Now, the total atomic number on the product side must add up to 90, which is the atomic number on the reactant side. We can write the equation as:
90=88+Z90 = 88 + Z90=88+Z
To find Z, we solve for it:
Z=90−88=2Z = 90 – 88 = 2Z=90−88=2
So, Z = 2.
Final Answer:
- A = 4
- Z = 2
Explanation:
In nuclear reactions, the mass number (A) represents the total number of nucleons (protons + neutrons) in the nucleus, while the atomic number (Z) represents the number of protons (or the element). The reaction must balance both the mass numbers and atomic numbers on either side. Thus, to maintain balance in this decay reaction, the missing values of A and Z in the product must be 4 and 2, respectively. The element with atomic number 2 is Helium (He), so the product would be 4/2He, which is an alpha particle.
