Which of the following should a student select to correctly represent an isotope of \( { }_{19}^{39} \mathrm{~K} \) ?

An isotope of an element is characterized by the same number of protons but a different number of neutrons. For potassium, which has an atomic number of 19, \( { }_{19}^{39} \mathrm{~K} \) has 19 protons and 20 neutrons (39 total nucleons - 19 protons = 20 neutrons). This means any isotope representation must maintain the atomic number (19) but can have different mass numbers by varying the neutrons. One alternative isotope could be \( { }_{19}^{40} \mathrm{~K} \), representing potassium with one extra neutron (40 total nucleons). Another example is \( { }_{19}^{38} \mathrm{~K} \), indicating potassium with one less neutron. They would still be considered isotopes of potassium due to having the same proton count!