The correct answer is option 4: "less than the number of electrons in the atom".

An anion is a negatively charged atom, which means it has gained one or more electrons. In an atom, the number of protons is equal to the atomic number of the element. However, when an atom gains electrons and becomes negatively charged, it now has more negatively charged electrons than positively charged protons. Therefore, the number of protons in a negatively charged atom (anion) is less than the number of electrons in the atom.

Option 1, "more than the atomic number of the element", is incorrect because the atomic number represents the number of protons in a neutral atom, not an anion.

Option 2, "less than the atomic number of the element", is also incorrect because the number of protons remains the same in an anion.

Option 3, "more than the number of electrons in the atom", is incorrect because the number of protons is equal to the number of electrons in a neutral atom, but in an anion, the number of protons is less than the number of electrons.

Therefore, the correct answer is option 4.