Let the number of protons be $p$ (which is equal to the atomic number $Z$) and the number of neutrons be $n$. According to the question: $n = p + \frac{19.23}{100}p = 1.1923 p$ The mass number ($A$) is the sum of protons and neutrons: $A = n + p = 1.1923 p + p = 2.1923 p$

Now, test the given atomic numbers:

1. For Iron ($Fe$), $Z = 26$: $A = 2.1923 \times 26 = 56.9998 \approx 57$ This corresponds to the isotope $^{57}Fe$.
2. For Cobalt ($Co$), $Z = 27$: $A = 2.1923 \times 27 = 59.19$ This does not result in a whole number close to the options ($^{57}Co$ or $^{60}Co$).

Thus, the correct element and mass number is $^{57}Fe$.