Consider the nuclear equation below.
${ }_{66}^{222} Rn \longrightarrow{ }_7^{218} Po+{ }_2^4 He$
Which is the missing value that will balance the equation?
A. 84
B. 86
C. 88
D. 90
Answer (2)
The problem requires balancing a nuclear equation to find the missing atomic number.
Set up the equation for the atomic numbers: 86 = Z + 2 .
Solve for Z: Z = 86 − 2 = 84 .
The missing atomic number is 84 .
Explanation
Understanding the Problem We are given a nuclear equation and asked to find the missing atomic number that will balance the equation. The equation is: 86 222 R n ⟶ Z 218 P o + 2 4 He We need to find the value of Z.
Setting up the Equations In a balanced nuclear equation, the sum of the mass numbers (the top number) and the sum of the atomic numbers (the bottom number) must be the same on both sides of the equation. In this case, we have: Mass numbers: 222 = 218 + 4 Atomic numbers: 86 = Z + 2
Solving for Z To find the missing atomic number Z, we can solve the equation: 86 = Z + 2 Subtract 2 from both sides: Z = 86 − 2 Z = 84
Final Answer Therefore, the missing atomic number is 84.
Examples
Nuclear equations are used in various applications, such as determining the age of ancient artifacts through carbon dating, understanding nuclear medicine procedures like PET scans, and designing nuclear reactors for power generation. Balancing nuclear equations ensures that the number of protons and neutrons is conserved, which is crucial for predicting the stability and behavior of radioactive materials. For example, in carbon dating, scientists use the decay of carbon-14 to estimate the age of organic materials. By understanding the nuclear equation for carbon-14 decay, they can accurately determine the amount of carbon-14 remaining in a sample and, consequently, its age. This technique is invaluable in archaeology and paleontology.
The missing atomic number that balances the nuclear equation is 84. This means the complete balanced equation features polonium with the atomic number of 84. Hence, the correct answer is option A: 84.
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