Creating a Decay Equation

Write the complete decay equation in $_{Z}^{A} X_{N}$ notation for beta decay producing $^{137} B a$ . Refer to the periodic table for values of Z.

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Strategy
Beta decay results in an increase in atomic number. As a result, the original (or parent) nucleus, must have an atomic number of one fewer proton.
Solution
The equation for beta decay is as follows

${}_{Z}^{A}X_{N} \to {}_{Z + 1}^{A}Y_{N - 1} + e + v .$
22.38

Considering that barium is the product (or daughter) nucleus and has an atomic number of 56, the original nucleus must be of an atomic number of 55. That corresponds to cesium, or Cs.

${}_{55}^{137}C s_{N} \to {}_{56}^{137}B a_{N - 1} + e + v$
22.39

The number of neutrons in the parent cesium and daughter barium can be determined by subtracting the atomic number from the mass number (137 – 55 for cesium, 137 – 56 for barium). Substitute those values for the N and N – 1 subscripts in the above equation.

${}_{55}^{137}C s_{82} \to {}_{56}^{137}B a_{81} + e + v$
22.40

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