Energy Levels in Atom - NEET Notes, Formula & Common Mistakes

What NEET Asks

• Direct calculation based on Bohr's energy formula for H-like species.
• Conceptual questions on ground state, excited states, and ionization energy.
• Problems involving electron transitions, emission/absorption spectra, and calculating energy/wavelength.

Key Points

• Quantized Energy: Electrons occupy specific, discrete energy levels (shells) around the nucleus, denoted by principal quantum number n (1, 2, 3...). Each level has a fixed energy.
• Ground State: The lowest energy state (n=1) where the electron is most stable. This is the natural, unexcited state.
• Excited State: Any energy state higher than the ground state (n > 1). Electrons reach here by absorbing energy.
• Energy Relation: Energy levels become closer as n increases. The energy $E_n \propto -1/n^2$ for H-like species. Higher 'n' means less negative (higher) energy.
• Electron Transitions: Electrons absorb energy to move to higher n (excitation) and emit energy (as photons) when moving to lower n (de-excitation), forming atomic spectra.
• Ionization Energy: Energy required to remove an electron completely from an atom (from n=1 to n=∞).

Must-Know Formula / Reaction

$E_n = -13.6 \frac{Z^2}{n^2}$ eV/atom

• $E_n$: Energy of electron in the $n^{th}$ orbit.
• Z: Atomic number of the H-like species (e.g., H, He⁺, Li²⁺).
• n: Principal quantum number (orbit number, e.g., 1 for ground state, 2 for first excited state).

Common Mistakes

• Students often forget to square the atomic number (Z) when dealing with H-like species other than hydrogen.
• Don't confuse emission (energy released, electron moves to lower n) with absorption (energy absorbed, electron moves to higher n). The sign of ΔE is crucial.
• Incorrectly applying the relationship between energy, frequency, and wavelength (e.g., longest wavelength corresponds to smallest energy difference).

Rapid Revision

Atomic energy levels are quantized, described by 'n'. The ground state (n=1) is lowest energy. Energy increases with 'n'. Electron transitions cause emission or absorption spectra. Remember $E_n = -13.6 \frac{Z^2}{n^2}$ eV for H-like atoms. Ionization means n=1 to n=∞.