ASTRONOMY FUNDAMENTALS - Chapter 1, Exercise 3 Solution
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Classifying Spectra with Kirchhoff & Bunsen's Laws

PROBLEM
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Classify each scenario as producing a continuous spectrum, an
emission-line spectrum, or an absorption-line spectrum, and explain why:
(a) a bare, glowing metal filament with nothing between it and the
    observer
(b) a thin cloud of hot hydrogen gas, viewed directly, with no light
    source behind it
(c) starlight passing through the star's own cooler outer atmosphere
    before reaching an observer's telescope

SOLUTION
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(a) Bare, glowing metal filament -> CONTINUOUS SPECTRUM

    A hot, solid, opaque object (a metal filament) produces light across
    a smooth, continuous range of wavelengths. Since nothing sits between
    the filament and the observer, there is nothing available to absorb
    specific wavelengths out of that light or add extra emission lines
    to it. This is Kirchhoff's first law: hot solid objects produce a
    continuous spectrum.

(b) Thin cloud of hot hydrogen gas, viewed directly -> EMISSION-LINE
    SPECTRUM

    A hot gas, viewed directly with no other light source behind it,
    emits light only at specific wavelengths determined by hydrogen's
    own atomic structure - not a smooth continuous spread. Against a
    dark background, this produces a spectrum showing a small number of
    bright, discrete lines. This is Kirchhoff's second law: hot gases
    produce an emission-line spectrum.

(c) Starlight passing through the star's own cooler outer atmosphere ->
    ABSORPTION-LINE SPECTRUM

    The star's own hot interior initially produces a continuous
    spectrum (case a). But that light then passes through the star's
    own cooler surrounding gas (its outer atmosphere) before reaching
    the observer. That cooler gas absorbs light specifically at the
    exact wavelengths it would otherwise emit if it were hot and
    glowing on its own - the same wavelengths as in case (b), but now
    missing from the light rather than added to it. The result is a
    near-continuous spectrum with dark absorption lines at those
    specific wavelengths. This is Kirchhoff's third law, and it is
    exactly the real mechanism behind Fraunhofer's own 574 observed
    dark lines in sunlight.

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WHY THIS WORKS AS AN ANSWER

All three cases follow directly from the same underlying real physics:
a continuous spectrum requires a hot, dense source with nothing
selectively absorbing or adding to the light; an emission spectrum
requires a hot, low-density gas emitting on its own; and an absorption
spectrum requires a continuous-spectrum source with a cooler gas
sitting between it and the observer. Case (c) is the one that actually
matches real starlight, which is why absorption spectroscopy - not
emission spectroscopy - is the real, standard method astronomers use to
determine a star's own chemical composition.