If an atom has 9 protons and 10 neutrons, what is its atomic number?
The number of neutrons is obtain through the difference of the mass number and the number of electrons.
By looking at the periodic table, you will see that Fluorine has 9 protons.
Since the number of electrons equal the number of protons, Fluorine has 9 electrons as well.
Meanwhile, it's mass number of 19, minus 10 neutrons, gives you 9 protons or electrons. Hence, the atom would be Fluorine.
As for the atomic number, it is obtainable through the periodic table itself.