No, an atom cannot exist with only protons and electrons. The reason is that atoms require a balance between the positively charged protons in the nucleus and the negatively charged electrons in order to be electrically neutral.
In an atom, the number of protons in the nucleus determines its atomic number and defines the element. For example, hydrogen has one proton, helium has two protons, and so on. Electrons, which carry a negative charge, orbit around the nucleus and occupy specific energy levels or orbitals.
The number of protons in an atom determines its positive charge, while the number of electrons determines its negative charge. In a neutral atom, the number of protons must be equal to the number of electrons to balance the charges. This balance of charges ensures that the atom is stable.
If an atom were to have only protons and no electrons, the positive charge from the protons would overwhelm the negative charge, resulting in a net positive charge. The atom would become an ion with a positive charge. Conversely, if an atom were to have only electrons and no protons, the negative charge from the electrons would dominate, resulting in a net negative charge, and it would also become an ion.
Therefore, for an atom to be electrically neutral, it must have an equal number of protons and electrons.