Question 24.1: Writing Equations for Nuclear Reactions Problem Write balanc......
Writing Equations for Nuclear Reactions
Problem Write balanced equations for the following nuclear reactions:
a. Naturally occurring thorium-232 undergoes α decay.
b. Zirconium-86 undergoes electron capture.
Plan We first write a skeleton equation that includes the mass numbers, atomic numbers, and symbols of all the particles on the correct sides of the equation, showing the unknown product particle as _Z^AX. Then, because the total of mass numbers and the total of atomic numbers must be equal on the left and right sides, we solve for A and Z, and use Z to determine X from the periodic table (Fig 1).
Solution (a) Writing the skeleton equation, with the α particle as a product:
^{232}_{90}Th ⟶ ^A_ZX + ^4_2α
Solving for A and Z and balancing the equation: For A, 232 = A + 4, so A = 228.
For Z, 90 = Z + 2, so Z = 88. From the periodic table (Fig 1), we see that the element with Z = 88 is radium (Ra). Thus, the balanced equation is
(b) Writing the skeleton equation, with the captured electron as a reactant:
^{86}_{40}Zr + _{−1}^0e ⟶ ^A_ZX
Solving for A and Z and balancing the equation: For A, 86 + 0 = A, so A = 86. For Z, 40 + (−1) = Z, so Z = 39. The element with Z = 39 is yttrium (Y), so we have
^{86}_{40}Zr + _{−1}^0e ⟶ ^{86}_{39}Y
Check Always read across superscripts and then across subscripts, with the yield arrow as an equal sign, to check your arithmetic. In part (a), for example, 232 = 228 + 4, and 90 = 88 + 2.
