Is there any effect in the mass of an atom if it becomes negatively charged?

I know that atomic mass and mass number are two different things but the change in electrons (although may not affect the mass number) may affect the atomic mass, wouldn't it?

Technically, adding an electron to an atom makes the atom and ion and adds the mass of an electron (about 9E-28 g which is quite small). but, yes, it does change. It does not affect the atomic number or the mass number but the atomic mass does change for ion but it is hardly worth taking into account.

When an atom becomes negatively charged, its overall charge is due to the gain of extra electrons. These electrons are negatively charged particles that orbit around the nucleus of an atom. However, the mass of an electron is extremely tiny compared to the mass of the protons and neutrons in the nucleus.

The atomic mass of an atom is determined by the sum of its protons and neutrons. Since the electrons have such a small mass compared to protons and neutrons, the addition or removal of electrons has a negligible effect on the atomic mass. In other words, whether an atom is neutral or negatively charged, its atomic mass remains essentially the same.

So, to answer your question, when an atom becomes negatively charged by gaining electrons, there is no significant effect on its mass. The atomic mass is primarily determined by the number of protons and neutrons in the nucleus, and the number of electrons surrounding the nucleus does not significantly contribute to the overall mass of the atom.