Two isotopes of potassium are k-37 and k-42. how many valence electrons are in an atom of k-42 in the ground state?

1 valence electron.

Explanation:

Isotopes are atoms of the same element which has different numbers of neutrons, and because of that have different masses number. K-37 has mass 37 amu, and K-42 has mass 42 amu.

The difference in neutrons doesn't change the number of protons either the number of electrons. Potassium is in group 1 in the periodic table, and all the elements in that group have one element in the valence shell, which is the last shell of the atom. So K-42 has 1 valence electron.