What Are Stars Made Of?: Going Further 9–12

Light is a mixture of colors

You know from Grade 10 that a prism spreads white light into a spectrum, red to violet Grade 10: Dispersion of light, and from Grade 9 that visible light is a small part of the electromagnetic spectrum Grade 9: Electromagnetic spectrum. Each color is light of a different wavelength, measured in nanometers (nm; 1 nm = 10⁻⁹ m):

Color	Wavelength (roughly)
violet	400–450 nm
blue	450–490 nm
green	490–565 nm
yellow	565–590 nm
orange	590–625 nm
red	625–700 nm

An instrument that spreads light out carefully enough for the wavelengths to be measured is a spectroscope. With one, you can see that not all light is the same mixture.

Three kinds of spectrum

Look at different lights through a spectroscope and you see three different kinds of spectrum.

A hot solid gives out every color: the wire in an old light bulb, a red-hot iron rod, the glowing coils of a heater. Its spectrum is a smooth band with no gaps, a continuous spectrum. (A hot, dense gas does the same, like the gas at the surface of the Sun.)
A hot, thin gas gives out only a few colors. Its spectrum is a few bright lines on a dark background, an emission spectrum. Each element has its own lines, at its own wavelengths, and no two elements have the same pattern.
When the light of a hot solid passes through a cool gas on its way to you, the gas takes out exactly the colors it would give out if it were hot. The spectrum is the full rainbow with dark lines across it, an absorption spectrum, and the dark lines are in the same places as that gas’s bright lines.

Figure 14.1 The three kinds of spectrum, for hydrogen. Hot hydrogen gives four bright lines; cool hydrogen in front of a hot filament takes out exactly those four colors.

These are known as Kirchhoff’s laws of spectra, after the German physicist who worked them out in 1859. The second and third are what make chemistry from far away possible: an element’s lines are its fingerprint, or its barcode, whether they shine bright or show up dark.

Each tube holds one gas, made to glow by electricity. Pick a gas and look at its light, spread out by a prism. Then try the hot filament.

Brightest lines: 434.0 nm (violet), 486.1 nm (blue-green), 656.3 nm (red)

Hydrogen glows pink-purple: its bright red line mixed with blue and violet ones. Only four lines in the visible part, the simplest pattern of any element, because hydrogen is the simplest atom.

You have probably seen sodium’s fingerprint at home. When salty dal boils over onto a gas flame, the flame flashes bright yellow: that is sodium, from the salt, giving out its two yellow lines. Other metals color a flame in their own way, which is how fireworks get their colors.

Nine small tins in a row, each with a flame of a different color: pink-red, red, orange, bright yellow, pale violet, green, blue-green, lilac and pale purple — **Figure 14.2** Flame colors. Each tin holds a different metal compound dissolved in methanol. From left: lithium (crimson), strontium (red), calcium (orange), sodium (yellow), barium (pale), boron (green), copper (blue-green), cesium and potassium (lilac). Photo: Hegelrast, CC BY-SA 4.0

A story from science

Two friends in Heidelberg

In the 1850s the chemist Robert Bunsen was testing which metals were in mineral water by the colors they gave a flame. His new gas burner, the Bunsen burner you may have used at school, had an almost colorless flame, so the colors showed clearly. But many metals gave similar colors. His friend, the physicist Gustav Kirchhoff, suggested looking at the flames through a prism. Every metal turned out to have its own pattern of bright lines.

In 1860 they saw two blue lines that belonged to no known element, in water from a spring at Dürkheim. They had found a new element, and called it cesium, from the Latin for “sky blue”. A year later, two dark red lines gave them rubidium, “deep red”. They had evaporated 40 tonnes of the spring water to get a few grams of cesium salt, but the lines had told them it was there before they had enough to see.

An old black-and-white photograph of three men in nineteenth-century suits, one seated between two standing — **Figure 14.3** Gustav Kirchhoff (left) and Robert Bunsen (seated), with their friend the chemist Henry Roscoe, around 1862. Photo: Henry Roscoe, Public domain

A street lamp gives a yellow light. Through a spectroscope you see one bright yellow line at 589 nm, and almost nothing else. What gas is in the lamp?

Pick an answer to see why.

Why each element has its own lines

Why should a gas give out only certain colors? The answer is inside its atoms.

You learned in Grade 9 that an atom’s electrons are in shells, and that the shells have different energies: the farther from the nucleus, the more energy. An electron can be in one shell or another, but never in between. So an electron in an atom can only have certain amounts of energy, called its energy levels, like the steps of a staircase: you can stand on a step, but not halfway between two.

When a gas is heated, or electricity passes through it, its atoms are knocked about and some electrons are pushed up to higher levels. They don’t stay there. Within a tiny fraction of a second each one drops back down, and gives out the energy it loses as a little packet of light, a photon.

The photon’s energy is exactly the difference between the two levels. And the energy of a photon decides its color. The German physicist Max Planck found in 1900 that the energy of light comes in packets of

$E = hf = \frac{hc}{\lambda}$

where f is the light’s frequency, λ its wavelength, c the speed of light (3.00 × 10⁸ m/s) and h a tiny number called Planck’s constant, 6.63 × 10⁻³⁴ J s. So more energy means a higher frequency and a shorter wavelength: a violet photon carries more energy than a red one.

Every atom of hydrogen has the same staircase, so every hydrogen atom can only make the same few drops, and give out the same few colors. Other elements have different staircases, and so different colors. That is the fingerprint.

Figure 14.4 The energy levels of the electron in a hydrogen atom, drawn to scale (1 electronvolt, eV, is 1.60 × 10⁻¹⁹ J). Drops that end on level 2 give out visible light: the bigger the drop, the shorter the wavelength. Drops to level 1 are much bigger and give ultraviolet light, which we can’t see.

Worked example

The energy of hydrogen’s red light

Hydrogen’s red line has a wavelength of 656.3 nm. (a) What is its frequency? (b) How much energy does one photon of it carry? (c) Show that this matches the drop from level 3 to level 2 in Figure 14.4.

Answer

a. From c = fλ:
$f = \frac{c}{\lambda} = \frac{3.00 \times 10^{8}\ \text{m/s}}{656.3 \times 10^{-9}\ \text{m}} = 4.57 \times 10^{14}\ \text{Hz}$
b.
$E = hf = 6.63 \times 10^{-34}\ \text{J s} \times 4.57 \times 10^{14}\ \text{Hz} = 3.03 \times 10^{-19}\ \text{J}$
c. In electronvolts: 3.03 × 10⁻¹⁹ J ÷ 1.60 × 10⁻¹⁹ J per eV = 1.89 eV. The drop from level 3 (−1.51 eV) to level 2 (−3.40 eV) is 3.40 − 1.51 = 1.89 eV. The same.

Try it

The blue-green line

The drop from level 4 (−0.85 eV) to level 2 (−3.40 eV) gives one of hydrogen’s lines. Work out the photon’s energy in joules, then its wavelength. Which line in Figure 14.4 is it?

Hint

The drop is 3.40 − 0.85 eV. Change it to joules, then use λ = hc ÷ E.

Answer

The drop is 3.40 − 0.85 = 2.55 eV = 2.55 × 1.60 × 10⁻¹⁹ = 4.08 × 10⁻¹⁹ J.
$\lambda = \frac{hc}{E} = \frac{6.63 \times 10^{-34} \times 3.00 \times 10^{8}}{4.08 \times 10^{-19}} = 4.88 \times 10^{-7}\ \text{m} = 488\ \text{nm}$
That is the blue-green line, measured at 486.1 nm. (The small difference comes from rounding the energies to two decimal places.)

The same staircase explains the dark lines. A cool hydrogen atom has its electron on a low step. Light of every color passes by, and the atom can only take a photon whose energy exactly fits one of its jumps up. So it takes exactly the colors it would give out coming down, and those colors go missing from the light that reaches you.

The barcode in sunlight

In 1814 the German glassmaker Joseph von Fraunhofer was testing the glass for telescope lenses. Looking at sunlight through a prism and a small telescope, he saw that the Sun’s rainbow was crossed by dark lines, hundreds of them. He mapped 574 of them, and labeled the strongest with letters, A to K. He had no idea what they were.

The Sun's visible spectrum cut into strips and stacked, red at the top to violet at the bottom, each strip crossed by many thin dark lines — **Figure 14.5** The Sun’s spectrum, from red (top left) to violet (bottom right), cut into strips so that it fits on a page. Each dark line is a color taken out by an element in the Sun’s outer layers. Photo: N.A. Sharp, NOAO/NSO/Kitt Peak FTS/AURA/NSF, CC BY 4.0

In 1859 Kirchhoff solved the puzzle. He noticed that two dark lines in the yellow, Fraunhofer’s D lines, were exactly where sodium’s two bright yellow lines are. Then he passed sunlight through a sodium flame, expecting the flame’s yellow light to fill the gaps in. Instead, the dark lines grew darker. The cooler sodium in the flame was taking out the same colors.

So the Sun’s dark lines are absorption lines. The Sun’s hot, dense surface gives out a continuous spectrum, and the cooler gas above it takes out the colors of the elements it contains. Sodium is in the Sun. So, Kirchhoff found, are iron, calcium, magnesium and others: elements we know on Earth, in the Sun, 150 million kilometers away.

Now it’s your turn to read a star.

Here are the spectra of three stars. Tap an element to lay its fingerprint, its lines as measured in a laboratory, under the star’s spectrum. If every one of its lines meets a dark line, that element is in the star. Pick the ones you think are there, then check. (Real spectra have thousands of lines; these show only the strongest.)

Tap the elements you think are in this star, then press Check. An element is there if every one of its lines meets a dark line.

Where do the dark lines in a star’s spectrum come from?

Pick an answer to see why.

Reading the stars

By 1900 astronomers had photographed the spectra of hundreds of thousands of stars, and sorted them by the pattern of their lines. Some showed very strong hydrogen lines, others weak ones; some showed helium, most didn’t. Most astronomers thought the differences showed what the stars were made of, and that stars were made of much the same mix as the Earth’s rocks, iron and all.

A story from science

The woman who found what stars are made of

Cecilia Payne was born in England in 1900. At Cambridge she heard a lecture about Einstein’s theory being tested in an eclipse, and decided to become an astronomer, though women there could study but not be given degrees. She moved to Harvard in the USA in 1923.

There she used new physics from India. In 1920 the Indian physicist Meghnad Saha had shown how heat strips electrons from atoms, and so changes which lines an element can make. A star’s lines, Payne realized, depend mostly on its temperature, not on what it is made of. Spica’s helium lines show because it is hot enough; the Sun has helium too, but is too cool to show it. Once she allowed for the temperature, the stars were all made of nearly the same things. And the result was startling: they were almost entirely hydrogen and helium. She worked out that there was about a million times more hydrogen in the stars than heavier elements.

It went against everything astronomers believed. The leading American astronomer, Henry Norris Russell, told her it was clearly impossible, and in her thesis of 1925 she wrote that her result was “almost certainly not real”. Four years later, Russell himself found the same thing in another way, and it is now known to be true: hydrogen and helium make up about 98% of the visible matter in the universe. Another astronomer called her thesis the most brilliant ever written in astronomy. In 1956 she became the first woman to be a full professor at Harvard.

A black-and-white photograph of a young woman in a knitted jumper, seated at a desk in an office with filing cabinets — **Figure 14.6** Cecilia Payne (later Payne-Gaposchkin) at Harvard College Observatory. Photo: Smithsonian Institution/Science Service, restored by Adam Cuerden, Public domain

A star’s spectrum tells us more than what it is made of:

Its temperature, from which lines are strong, and from its color (the colors of stars, red to blue, from Grade 9).
How it moves. If a star moves towards us or away, all its lines shift a little, towards blue or towards red. That shift is how we know the universe is expanding: the next topic.
Whether it has a hidden partner. A star with an unseen planet or star going round it wobbles, and its lines shift back and forth.

Make a spectroscope

Activity

A spectroscope from an old CD

You need: an old CD or DVD you no longer want, a cardboard box about the size of a shoebox (or a long biscuit box), scissors, black tape, and some different lights: a tube light or a white CFL bulb, an LED bulb, a phone’s torch, and if you can find one, an old yellow street lamp or a candle flame.

At one end of the box, cut a very narrow slit, about 1 mm wide and 3 cm long. (Two pieces of black tape with a gap between them make a neat slit.)
At the other end, cut a window about 3 cm across, near one corner.
Tape the CD inside the box, below the window, shiny side up, tilted at about 60° so that light from the slit falls on it.
Point the slit at a tube light from about a meter away, and look in through the window at the CD. Turn the box until you see a spectrum.
Look at each light in turn, and draw what you see.

Never point it at the Sun. Look at sunlight only as it reflects from a white wall or a cloud.

What you should see

The CD’s tightly packed tracks, about 1.6 µm apart, spread light into its colors just as a prism does. A tube light or CFL shows separate bright lines: violet, blue, a bright green (546 nm) and yellow, the lines of mercury, on top of a fainter smooth band from the white coating inside the tube. An old filament bulb or a candle gives a smooth rainbow with no lines. An LED gives a smooth spectrum too, often with a bright patch in the blue. A sodium street lamp gives mostly one yellow line. Pointed at a white wall in daylight, a well-made box may even show the strongest of the Sun’s dark lines.

A CD lying on a table, its surface showing bright bands of rainbow colors — **Figure 14.7** The surface of a CD splits light into its colors, because its tracks are so close together. Photo: Yann Droneaud from Paris, France, CC BY-SA 2.0

In short

White light is a mixture of wavelengths; a prism or a spectroscope spreads them out into a spectrum.
A hot solid or dense gas gives a continuous spectrum; a hot, thin gas gives bright lines, an emission spectrum; a cool gas in front of a hot source takes out the same colors, giving dark lines, an absorption spectrum.
Each element’s lines are at its own wavelengths, its fingerprint, because its electrons can only have certain energies. A photon’s energy is E = hf = hc/λ, equal to the drop between two levels.
The dark lines in sunlight and starlight show which elements are in the stars. Helium was found in the Sun this way, 27 years before it was found on Earth.
Which lines a star shows depends mostly on its temperature. Allowing for that, Cecilia Payne found in 1925 that stars are almost entirely hydrogen and helium.

Questions

A star’s spectrum shows strong hydrogen lines but no helium lines. What can you say about helium in the star?

Pick an answer to see why.

a.

Why does a light bulb’s filament give a continuous spectrum, but a tube of hot hydrogen gives only four bright lines?

Answer

In a thin gas, the atoms are far apart, and each gives out light on its own, only in the drops its electrons can make between their fixed energy levels: so only a few wavelengths, hydrogen’s four visible lines. In a hot solid, the atoms are packed tightly and jostle each other, so their energy levels are smeared out and the light is given out at every wavelength: a continuous spectrum.

b.

Explain why the dark lines of an element in an absorption spectrum are at exactly the same wavelengths as the bright lines in its emission spectrum.

Answer

Both come from the same jumps between the same energy levels. When an electron drops from a higher level to a lower one, the atom gives out a photon whose energy is the difference between the levels. When an electron is on the lower level, the atom can absorb only a photon with exactly that energy, to jump up. Equal energies mean equal wavelengths (E = hc/λ), so the colors taken out of the light are the same as the colors a hot gas of that element gives out.

c.

Hydrogen’s violet line has a wavelength of 410.2 nm. Calculate (i) its frequency and (ii) the energy of one photon of it. (iii) Is this more or less energy than a photon of hydrogen’s red line, 3.03 × 10⁻¹⁹ J? Why?

Answer

i.f = c ÷ λ = 3.00 × 10⁸ ÷ (410.2 × 10⁻⁹) = 7.31 × 10¹⁴ Hz.
ii.E = hf = 6.63 × 10⁻³⁴ × 7.31 × 10¹⁴ = 4.85 × 10⁻¹⁹ J.
iii.More: violet light has a shorter wavelength, so a higher frequency, and a photon’s energy is proportional to its frequency. In the atom, the violet line comes from the biggest drop of the four, from level 6 to level 2.

d.

How was helium discovered in the Sun before it was found on Earth?

Answer

During the total eclipse of the Sun on 18 August 1868, seen from India, astronomers looked at the glowing gas around the edge of the hidden Sun through spectroscopes. They saw a bright yellow line at 587.6 nm that matched the lines of no known element; it was near sodium’s yellow lines, but not on them. Norman Lockyer concluded that it came from a new element and named it helium, after the Greek helios, the Sun. It was found on Earth only in 1895, by William Ramsay.

e.

The Sun is about 150 million kilometers away and nobody has taken a sample of it. Explain, step by step, how we know there is sodium in it.

Answer

Sodium heated in a flame in a laboratory gives out two bright yellow lines, at 589.0 and 589.6 nm: its fingerprint.
Sunlight spread out by a spectroscope shows dark lines at exactly 589.0 and 589.6 nm (Fraunhofer’s D lines).
A cool gas takes out of light exactly the wavelengths it gives out when hot (Kirchhoff showed this by passing sunlight through a sodium flame: the D lines grew darker).
So the D lines are made by sodium in the cooler outer layers of the Sun, taking those colors out of the light from the hot surface below.

Where to go next

How do we know the universe is expanding? The lines in the light of distant galaxies are all shifted towards red. How that tells us the galaxies are moving away, and the universe is growing.
How do we find planets around other stars? The wobble in a star’s lines is one of the ways astronomers have found thousands of them.
Where did the atoms in your body come from? The stars are mostly hydrogen and helium. So where did the carbon, oxygen and calcium in you come from?