Types of spectra

Continuous spectrum. White light — from the Sun, an incandescent filament, or any sufficiently hot solid, liquid, or dense gas — contains photons of essentially every wavelength in the visible range. Dispersed by a prism, it spreads into an unbroken band merging smoothly from violet to red, exactly like a rainbow. Nothing about a continuous spectrum identifies which element produced it; it depends only on temperature.

Line (atomic) spectrum. Atoms of a single element in the gaseous state, excited by an electric discharge at low pressure or by heating a volatile salt in a flame, emit light only at certain specific wavelengths, never a continuous range. Passed through a prism, this becomes a series of sharp bright lines against a dark background — a line spectrum, also called an atomic spectrum. Every element has its own unique pattern of lines, as distinctive as a fingerprint, which is why flame tests and astronomical spectroscopy can identify elements from their light alone.

Emission versus absorption spectra. An emission spectrum is the light directly given off by a glowing source — continuous if the source is hot and dense, or a line spectrum if it is an excited low-pressure atomic gas. An absorption spectrum is produced instead when white light passes through a cooler gas of some element on its way to the observer: the gas absorbs exactly the wavelengths it would itself emit if excited, so those wavelengths vanish from the transmitted beam and show up as dark lines at precisely the same positions the bright emission lines would occupy. Emission and absorption line spectra of a given element therefore share identical line positions; only the appearance — bright lines on dark, or dark lines on bright — differs.

Why the lines are discrete: the quantum link. A photon is emitted only when an electron falls from a higher allowed energy level $E_i$ to a lower one $E_f$, and the photon carries away exactly that energy difference:

where: $E_{\text{photon}}$ is the photon's energy (joules), $h = 6.626\times10^{-34}\ \text{J s}$ is Planck's constant, $\nu$ is the photon's frequency (hertz), $c = 3.0\times10^8\ \text{m s}^{-1}$ is the speed of light, $\lambda$ is the emitted wavelength (metres), and $E_i - E_f$ is the fixed energy gap between two allowed levels of the atom. Because an atom has only a discrete set of allowed levels, only a discrete set of energy gaps $E_i - E_f$ exists, and therefore only a discrete set of photon wavelengths can ever be emitted — this is exactly why a line spectrum is made of sharp lines rather than a smear of colour. If electron energies could vary continuously, as Rutherford's model implicitly allowed, every possible energy gap would occur and the spectrum would be continuous, just like sunlight; the observed discreteness is the direct experimental fingerprint of quantisation, and it is the fact Bohr's model was built to explain.

Question. Two sealed glass tubes contain low-pressure hydrogen gas and low-pressure neon gas, each excited by an electric discharge. (a) Explain why the two tubes produce different, but each individually reproducible, line patterns when their light is passed through a prism. (b) The hydrogen tube's red line sits at $656\ \text{nm}$. Find the energy, in joules and electronvolts, of the photons making up that line.

Step 1. In each tube, the discharge raises atoms to higher energy levels; as they relax back down, each atom emits a photon whose energy equals the exact difference between the two levels involved, following $E_{\text{photon}} = hc/\lambda$.

Step 2. Because each element has its own distinct, intrinsic set of allowed electron energy levels, the set of possible energy gaps — and hence possible emitted wavelengths — differs from element to element. Hydrogen therefore shows one specific set of sharp lines (including the $656$, $486$, $434$ and $410\ \text{nm}$ Balmer lines), while neon shows an entirely different set (the basis of orange-red neon signs).

Step 3. Since each element's energy levels are fixed, unchanging properties of the atom, the same discharge conditions reproduce exactly the same line pattern every time — this reproducibility is what makes line spectra usable as fingerprints for identification.

Step 4. For the $656\ \text{nm}$ hydrogen line: $E_{\text{photon}} = \dfrac{hc}{\lambda} = \dfrac{(6.626\times10^{-34})(3.0\times10^{8})}{656\times10^{-9}} = 3.03\times10^{-19}\ \text{J}$, which is $3.03\times10^{-19}/1.602\times10^{-19} = 1.89\ \text{eV}$. The two gases give different, reproducible line patterns because each element has its own fixed set of energy levels, and the hydrogen red line at 656 nm carries a photon energy of 3.03 × 10⁻¹⁹ J, or 1.89 eV.

• Confusing a continuous spectrum (hot solid, liquid, or dense gas; unbroken band of colour) with a line spectrum (excited low-pressure atomic gas; discrete sharp lines) — the source and the mechanism are entirely different.
• Thinking emission and absorption line spectra of the same element occur at different wavelengths — they occur at exactly the same wavelengths; only bright-on-dark versus dark-on-bright differs.
• Believing a line spectrum shows atoms can have any energy — it shows the opposite: discreteness in the spectrum is direct evidence that only certain, quantised energies are allowed.
• Plugging wavelength directly into $E = h\nu$ without first converting to frequency via $\nu = c/\lambda$, or mixing joules and electronvolts without converting consistently.

Ask the tutor: curious how the exact positions of the Balmer lines connect to the Rydberg equation and Bohr's allowed energy levels — ask the AI tutor to bridge this topic into Bohr's atomic model.