Answer
$^{38}_{19}K\rightarrow\,^{38}_{18}Ar+\,^{0}_{1}e$
Work Step by Step
Let the element that undergoes radioactive decay be $X$, its mass number be $A$ and let the atomic number be $Z$.
We know that a positron is a positively charged electron, that is, $^{0}_{1}e$.
As argon-38 is formed by positron emission, we can write
$^{A}_{Z}X\rightarrow\,^{38}_{18}Ar+\,^{0}_{1}e$
As the sum of masses and charges should be equal on both the sides, we have
$A=38+0=38$
$Z=18+1=19$
The element with atomic number $Z=19$ is potassium with the symbol $K$.
Therefore, the required balanced nuclear equation is
$^{38}_{19}K\rightarrow\,^{38}_{18}Ar+\,^{0}_{1}e$
