An astronomer observes a gas cloud that produces dark absorption lines in an otherwise continuous spectrum. A lab scientist heats a sample of the same element and records its emission spectrum. How do the two sets of spectral lines compare?
AThe emission lines are at longer wavelengths than the absorption lines — emission releases less energy than absorption requires
BThe emission lines are at shorter wavelengths — the cold gas absorbs high-energy photons that the hot gas cannot produce
CThe emission lines are at identical wavelengths to the absorption lines — both involve the same atomic energy-level transitions
DThe lines are at completely different wavelengths — emission and absorption involve different types of electron transitions
Emission and absorption are the same atomic transition running in opposite directions. An atom emits a photon when an electron falls from a higher to a lower energy level; it absorbs a photon of identical energy when the electron is excited from that lower level back up to the higher one. The photon energy — and therefore the wavelength — is determined by ΔE = hc/λ, which is the same for both processes. This is why dark Fraunhofer absorption lines in sunlight are at exactly the same wavelengths as the bright emission lines of the same elements in a laboratory flame.
Question 2 Multiple Choice
Classical physics predicted that heated atoms should radiate light continuously across all wavelengths. Why was the discovery of discrete spectral lines such a problem for this prediction?
AClassical physics predicted absorption but not emission, so the existence of emission lines was entirely unexpected
BThe Rydberg formula expressed spectral wavelengths using integer quantum numbers — discrete integers cannot emerge naturally from any continuous classical model
CClassical physics predicted only metals could emit visible light when heated, so gas emission lines violated this prediction
DClassical physics predicted spectral lines at the same wavelengths for all elements, so element-specific lines were anomalous
Classical electromagnetic theory predicted that an accelerating charge (an electron in an atom) should radiate continuously across all frequencies. Instead, each element emitted only a discrete set of wavelengths, and Rydberg's formula showed these wavelengths were governed by integer pairs (n₁, n₂). There is no way to derive integers from a continuous classical model. The discreteness was the crucial clue pointing toward quantized energy levels inside atoms — a concept entirely foreign to classical physics.
Question 3 True / False
The dark Fraunhofer lines in sunlight are at exactly the same wavelengths as the bright emission lines seen when the same elements are heated in a laboratory.
TTrue
FFalse
Answer: True
This identity is the foundation of spectroscopic composition analysis. A cool gas absorbs exactly the photon energies it would emit when hot, because both processes involve the same atomic energy-level transitions. The sun's outer atmosphere absorbs specific wavelengths from the continuous radiation produced by the hot interior, leaving dark gaps. Matching those gaps to laboratory emission lines identifies the elements present — allowing us to determine the chemical composition of the sun and distant stars without physically sampling them.
Question 4 True / False
The Balmer series, Lyman series, and Paschen series in hydrogen involve three different types of hydrogen atoms undergoing distinct internal transitions.
TTrue
FFalse
Answer: False
All three series come from the same hydrogen atom. The difference is which lower energy level the electron transitions into, not the type of atom or transition. Lyman series (UV): transitions fall to n = 1 (ground state). Balmer series (visible): transitions fall to n = 2. Paschen series (IR): transitions fall to n = 3. A single hydrogen atom can produce lines from all three series depending on which higher level it was excited to and which lower level it falls back to.
Question 5 Short Answer
Why do discrete emission spectra — rather than continuous emission — imply that atoms have discrete internal energy levels?
Think about your answer, then reveal below.
Model answer: A photon's energy is fixed by its wavelength: E = hc/λ. For an atom to emit a photon of a specific wavelength, it must release exactly that amount of energy. If atoms could exist at any energy, they could release photons of any wavelength, producing a continuous spectrum. The fact that only certain discrete wavelengths are emitted means the atom can only release certain fixed amounts of energy — which means it can only occupy certain discrete internal energy states. Each spectral line is a readout of one specific allowed energy-level transition.
This logic runs in both directions: discrete spectra imply discrete energy levels, and discrete energy levels predict discrete spectra. The Bohr model you will study next derives these energy levels from first principles and reproduces the Rydberg formula, confirming that the observed spectral integers n₁ and n₂ are quantum numbers labeling those levels.