The atomic symbol for the unknown nuclide in the decay of Radium-221 is X⁸⁶¹⁹⁷, where X represents the element symbol, Z is the atomic number, and A is the mass number.
To determine the atomic symbol for the unknown nuclide in the decay of Radium-221 (Ra-221), we need to break down the equation and identify the unknown nuclide, which is represented as Xᶻᴬ. The given decay equation is:
Ra⁸₂²¹ → He²⁴ + Xᶻᴬ
Here's the step-by-step process to find the atomic symbol for the unknown nuclide Xᶻᴬ:
1. Identify the Parent Nuclide:
- The parent nuclide in this equation is Radium-221 (Ra-221). Its atomic number (Z) is 88, and its mass number (A) is 221.
2. Identify the Daughter Nuclide:
- The daughter nuclide is Helium-24 (He-24). Its atomic number (Z) is 2, and its mass number (A) is 24.
3. Determine the Missing Values:
- We know that during the radioactive decay, the sum of atomic numbers (Z) and the sum of mass numbers (A) must be conserved. Therefore, we can calculate the missing values for the unknown nuclide Xᶻᴬ:
- Z for X = Z for Ra - Z for He = 88 - 2 = 86
- A for X = A for Ra - A for He = 221 - 24 = 197
4. Write the Atomic Symbol for the Unknown Nuclide:
- Now that we have determined the missing values, we can write the atomic symbol for the unknown nuclide Xᶻᴬ:
X⁸⁶¹⁹⁷