Final answer:
The orbital energy of a hydrogen-like atom decreases as the atomic number increases. Energy is conserved during transitions through photon emission, with longer wavelengths emitted for larger n values. Atomic number and principal quantum number both affect orbital energies and atom stability.
Step-by-step explanation:
The orbital energy of a hydrogen-like atom changes as it increases in atomic number; specifically, it decreases. This is because, in hydrogen-like atoms with a higher atomic number, the nucleus has more protons, which means a stronger nuclear charge. The increased nuclear charge exerts a greater attractive force on the electron, pulling it closer to the nucleus and resulting in lower energy orbitals that are more tightly bound to the nucleus.
When an atom makes a transition from a higher to a lower energy state, energy conservation is achieved by the emission of a photon, which carries away the energy difference between the two states. If an electron transitions from the (n+1)th orbit to the nth orbit, the wavelength of the emitted photon will be longer for larger values of n, because the energy difference between orbits decreases as n increases.
Overall, for a hydrogen-like atom, as the principal quantum number, n, increases, the orbital energy increases, because the electron is at a greater distance from the nucleus. However, as the atomic number increases, the most stable orbitals (those closest to the nucleus) have lower energy due to the increased nuclear charge.