Hail Mary Science
Light, heat and climate

Interactive electromagnetic spectrum

X-rays, visible light, infrared and radio waves are all the same thing: light with different wavelengths. Move the slider across the whole spectrum to see which region you are in and what that radiation does or is used for.

Key formula

f = c / λ · E = h · f = h · c / λ · λ_peak = 2,898 μm·K / T

Try it

How to use the simulator

The viewer sweeps the whole electromagnetic spectrum on a logarithmic scale, from X-rays (nanometers) to radio waves (kilometers). It's all light; only the wavelength changes. The readout tells you which region you're in and what that radiation is used for or does.

Controls

  • Wavelength slider: each step along the track multiplies the wavelength by ten.
  • "Petrova frequency" button: jumps to 25.984 μm, the wavelength the novel ties to astrophages.

Things to try

  1. Slide through the visible band (0.4–0.7 μm) and notice how narrow it is: our eyes see only a sliver of the spectrum.
  2. Press the Petrova button and confirm that it lands in the thermal infrared, invisible to us but easy for instruments to pick up.
  3. Compare 10 μm, where a room-temperature object glows brightest, with 0.5 μm, the Sun's peak. Wavelength reveals the temperature of the source.

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One thing, many names

Light is a wave of electric and magnetic fields traveling at 300,000 km/s. What changes from one kind of radiation to another is the wavelength, the distance between two crests. It runs from under a billionth of a meter for gamma rays to kilometers for long radio waves.

Our eyes see only a very narrow band, from about 380 to 750 nanometers. Everything else is invisible to us, but instruments pick it up easily.

Wavelength and energy

The shorter the wavelength, the more energy each photon carries. A photon of green light has about 2.5 electronvolts; an X-ray photon, thousands. Above roughly 10 eV radiation can knock electrons off atoms (it is ionizing), which is why X-rays and far ultraviolet damage DNA while radio and infrared don't.

Wavelength also reveals the temperature of the source. By Wien's law, a hot body glows brightest at a wavelength inversely proportional to its temperature. The Sun, at about 5,800 K, shines mostly in the visible; a person, at 310 K, in the infrared around 9 microns.

Worked example

Example: 25.98-micron light

  1. Frequency: f = 3·10⁸ / 25.98·10⁻⁶ ≈ 1.15·10¹³ Hz, about 11.5 terahertz.
  2. Energy per photon: E = h · f ≈ 7.6·10⁻²¹ J ≈ 0.048 eV, about 50 times less than a visible-light photon.
  3. By Wien's law, a body glowing brightest at that wavelength would be at 2,898 / 25.98 ≈ 112 K (about −161 °C).
  4. Press the viewer's Petrova button to jump to that wavelength and check that it lands in the thermal infrared.

In Project Hail Mary

The novel revolves around infrared light at one very specific wavelength, the "Petrova line", which gives away a fictional microorganism. The viewer lets you place it on the spectrum.

This tool appears in:Chapter 1The Awakening

Frequently asked questions

Why can't we see infrared?

Because the proteins in our retina only respond to photons with enough energy, between violet and red. Some snakes have organs that sense the thermal infrared of their prey.

Are phone signals dangerous?

They are radio waves, with photons millions of times less energetic than ultraviolet. They are not ionizing: their only proven effect is very slight heating.

Why does the James Webb telescope observe in infrared?

Because light from the most distant galaxies arrives stretched into the infrared by the expansion of the universe, and because infrared passes through the dust clouds where stars form.

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