Consider the nuclear equation below.
${ }_{66}^{222} Rn \longrightarrow{ }_{84}^{210} Po+{ }_2^4 He$
Which is the missing value that will balance the equation?
A. 84
B. 86
C. 88
D. 90
Answer (2)
Balance the atomic numbers in the nuclear equation.
Set up the equation: Z = 84 + 2 .
Solve for Z: Z = 86 .
The missing value is 86 .
Explanation
Understanding the Nuclear Equation Let's analyze the given nuclear equation: Z 222 R n ⟶ 84 210 P o + 2 4 He We need to find the atomic number (Z) of Radon (Rn) that will balance the equation. In a balanced nuclear equation, the sum of the atomic numbers and mass numbers on both sides must be equal.
Balancing Atomic Numbers To balance the equation, we need to ensure that the sum of the atomic numbers on the right side equals the atomic number of Radon on the left side. Therefore, we can set up the following equation: Z = 84 + 2
Finding the Missing Value Now, we solve for Z: Z = 86 So, the missing value that will balance the equation is 86.
Balanced Equation Therefore, the balanced nuclear equation is: 86 222 R n ⟶ 84 210 P o + 2 4 He
Examples
Nuclear equations are used in various fields, such as nuclear medicine for diagnostic imaging and cancer treatment, and in nuclear power plants for energy production. Balancing nuclear equations ensures that the number of protons and neutrons is conserved, which is crucial for understanding and predicting the behavior of radioactive materials. For example, in cancer treatment, radioactive isotopes are used to target and destroy cancer cells. Balancing the nuclear equation helps determine the type and amount of radiation emitted, ensuring effective and safe treatment.
To balance the nuclear equation, we find that the missing atomic number is 86. This is calculated by adding the atomic numbers of Polonium (84) and Helium (2). Therefore, the correct answer is option B: 86.
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