[27] Light, Spectra & Blackbody

List the EM spectrum regions in order from longest to shortest wavelength.

Radio, microwave, infrared, visible, ultraviolet, X-ray, gamma ray.

Which EM region carries the highest-energy photons, and which the lowest?

Gamma rays carry the most, radio waves the least (photon energy rises as wavelength shrinks).

What equation links the speed of light c, wavelength λ and frequency f of an EM wave?

c = λf, with c = 3.00 × 10⁸ m/s in vacuum, so wavelength and frequency are inversely proportional.

If the wavelength of an EM wave doubles, what happens to its frequency and to the energy of each photon?

Both are cut in half (c = λf and E = hf).

What equation gives the energy of one photon, in terms of frequency and of wavelength?

E = hf = hc/λ, where h is Planck's constant.

What is the value of Planck's constant h (the h in E = hf)?

6.626 × 10⁻³⁴ J·s.

Trap question: which EM region has the highest RATIO of frequency to wavelength (microwave, visible, infrared, radio, or all the same)?

Visible, the highest frequency of those options. It is the PRODUCT fλ = c that is the same for all.

What wavelength range is visible light?

About 0.4 to 0.7 µm (400 to 700 nm), from violet at the short end to red at the long end.

Roughly what wavelengths are blue, green and red light?

Blue about 450 nm, green about 550 nm, red about 650 nm.

What wavelength range do remote sensing tests use for the near infrared (NIR)?

About 0.7 to 1.3 µm.

What wavelength range do remote sensing tests use for the shortwave infrared (SWIR)?

About 1.3 to 3 µm.

What wavelength range do remote sensing tests use for the mid-wave infrared (MWIR)?

About 3 to 8 µm (the clearest part of it is 3 to 5 µm).

What wavelength range do remote sensing tests use for the thermal infrared (TIR)?

About 8 to 15 µm, where Earth-temperature objects emit most strongly.

List the infrared subregions in order from shortest to longest wavelength.

Near IR (NIR), shortwave IR (SWIR), mid-wave IR (MWIR), thermal IR (TIR), then far IR beyond about 15 µm.

Satellite bands at 1.6 µm and 2.2 µm lie in which infrared subregion?

Shortwave infrared (SWIR).

A satellite band at 3.9 µm lies in which infrared subregion?

Mid-wave infrared (MWIR), often just called mid-IR.

What wavelength range, and roughly what frequency range, is the microwave region?

About 1 mm to 1 m (roughly 300 GHz down to 300 MHz).

What wavelength range is ultraviolet (UV)?

About 10 to 400 nm.

What are the wavelength ranges of UV-A, UV-B and UV-C?

UV-A 315 to 400 nm, UV-B 280 to 315 nm, UV-C 100 to 280 nm.

Which EM region does a wavelength of 103.5 nm fall in?

Ultraviolet (far UV, inside the UV-C range).

Which UV band reaches Earth's surface in the greatest amount?

UV-A, because ozone barely absorbs it.

Which UV band is mostly, but not completely, absorbed by stratospheric ozone, so that the rest causes sunburn?

UV-B.

Which UV band is completely absorbed high in the atmosphere, and by which gases?

UV-C, absorbed by O₂ and O₃.

Is a 625 MHz EM wave visible light? If not, what is it?

No. λ = c/f = 0.48 m, a UHF radio wave (some charts call it microwave), so it has no color.

What quick rule converts a microwave frequency in GHz to a wavelength in cm?

λ (cm) ≈ 30 / f (GHz). Example: a 94 GHz radar has λ ≈ 0.32 cm (3.2 mm).

Radar bands (P, L, S, C, X, Ku, Ka, W) all lie in which EM region?

Microwave (about 1 mm to 1 m).

Which three EM regions supply most satellite Earth-observation data, and why not X-rays or gamma rays?

Visible, infrared and microwave, where the atmosphere is fairly transparent. X-rays and gamma rays are absorbed high in the atmosphere.

Below roughly what wavelength is the radiation a satellite receives from Earth mostly reflected sunlight, and above roughly what wavelength mostly Earth's own emission?

Reflected below about 3 µm, emitted above about 4 to 5 µm (the 3 to 5 µm region is a mix).

A sensor has channels at 0.65 µm, 1.6 µm and 11 µm. Which measure reflected sunlight and which measure radiation emitted by Earth?

0.65 and 1.6 µm measure reflected sunlight. 11 µm measures emitted thermal radiation.

Why can thermal infrared and passive microwave sensors (passive means they only receive radiation and send none out) collect data at night when a visible sensor cannot?

They detect radiation emitted by Earth itself, which needs no sunlight.

What is the best spectral region for mapping cloud-top temperature at night?

Thermal IR (about 10 to 12 µm), because it senses emitted radiation.

What does an ideal blackbody do with the radiation that falls on it?

It absorbs all of it at every wavelength (absorptivity 1, reflectance 0), and it is also the perfect emitter.

What does an object's emissivity (ε) measure?

How much it emits compared with a blackbody at the same temperature, from 0 to 1.

What is the emissivity of a blackbody?

Exactly 1, at all wavelengths.

True or false: perfect blackbodies exist in nature.

False. Real objects have ε below 1, though water and vegetation come close in the thermal IR (about 0.98).

Which best approximates an ideal blackbody: polished metal, a white sheet, or a cavity with a small opening?

The cavity with a small hole, because light that enters bounces around inside until it is absorbed.

Which everyday object is closest to a blackbody: a white roof, a black awning, a glass window, or metal siding?

The black (matte) awning. Dark matte surfaces absorb almost everything, while white and shiny surfaces reflect.

What is a graybody?

An object whose emissivity is below 1 and the same at all wavelengths.

What is a "white body"?

An ideal object with emissivity 0, which reflects all incident radiation.

Why does a 5500 K graybody (ε = 0.6) peak at the same wavelength as a 5500 K blackbody, even though it emits less?

Peak wavelength depends only on temperature. Emissivity just scales the whole curve down by the same factor at every wavelength.

An object at a fixed temperature changes from a blackbody to a graybody. How does its emitted power per unit area change?

It decreases. A graybody emits only the fraction ε (below 1) of what a blackbody at the same temperature emits.

Blackbody (Planck) curves plot spectral radiance against wavelength. What does spectral radiance describe, in plain words?

How much power a surface sends out at one particular wavelength (per unit area, per direction and per unit wavelength).

What law gives a blackbody's spectral radiance as a function of wavelength and temperature?

Planck's law (the Planck function).

What single property of a blackbody sets the shape of its emission spectrum?

Its absolute temperature. Size changes only the total power, not the spectrum's shape or peak.

Which law says a hotter blackbody emits more than a cooler one at every wavelength (its curves never cross)?

Planck's law.

How do the Planck curves of a hotter and a cooler blackbody differ?

The hotter curve is higher at every wavelength and peaks at a shorter wavelength.

On a graph of blackbody (Planck) curves, what feature represents each body's total emitted energy?

The area under its curve.

Which law gives blackbody spectral radiance proportional to T and to 1/λ⁴?

The Rayleigh-Jeans law (the long-wavelength approximation of Planck's law).

What is the value of Boltzmann's constant k (it appears in the Rayleigh-Jeans and Planck formulas)?

1.381 × 10⁻²³ J/K.

In what wavelength range is the Rayleigh-Jeans law a good approximation of Planck's law?

Long wavelengths (low frequencies, such as microwave). It fails badly at short wavelengths.

How does spectral radiance depend on temperature in the Rayleigh-Jeans law?

Linearly (directly proportional to T).

What is the "ultraviolet catastrophe"?

The classical Rayleigh-Jeans law predicts blackbody emission growing without limit at short wavelengths, which is impossible.

Which law fixed the ultraviolet catastrophe of the Rayleigh-Jeans law?

Planck's law, which uses both wavelength and temperature.

What was Planck's key assumption that made blackbody theory work?

Oscillator energy comes only in discrete quanta, E = hf.

State Wien's displacement law.

λmax = b / T: the peak emission wavelength equals Wien's constant b divided by the absolute temperature (in kelvin).

What is the value of Wien's constant b, in µm·K and in m·K?

2898 µm·K = 2.898 × 10⁻³ m·K.

Before plugging a temperature given in °C or °F into Wien's law or any other blackbody law, what must you do?

Convert it to kelvin (K = °C + 273.15).

How is Wien's law obtained from the Planck function?

Wien's law is the location of the curve's peak (where its slope is zero).

A blackbody's emission peaks near 10 µm. Roughly what is its temperature?

About 290 K, like Earth's surface (T = 2898 / 10).

Fill in: the peak wavelength of a blackbody is ___ ___ to its absolute temperature.

Inversely proportional.

If a surface's temperature increases, what happens to its peak emission wavelength?

It gets shorter (Wien's law).

If a blackbody's absolute temperature doubles, what happens to its peak wavelength?

It is cut in half.

A metal bar glows dull red, then bright white as it gets hotter. How does Wien's law explain this?

As temperature rises the emission peak shifts to shorter wavelengths, filling more of the visible band.

Why do stars have different colors, and which color is hottest?

Color follows surface temperature (Wien's law). Blue stars are hottest and red stars coolest.

Near what wavelength does the Sun's emission peak, and in what region is that?

About 0.5 µm (500 nm), blue-green visible light.

What is the Sun's effective surface temperature?

About 5772 K (often rounded to 5800 K).

A star's emission peaks near 0.5 µm. Roughly what is its surface temperature?

About 5800 K, like the Sun (2898 / 0.5 ≈ 5800).

Near what wavelength does Earth's surface (about 288 K) emit most strongly?

About 10 µm, in the thermal infrared.

Earth's effective radiating temperature (how warm it looks from space) is 255 K. Near what wavelength does that emission peak?

About 11 µm (2898 / 255 ≈ 11.4 µm).

Objects near room or body temperature (about 290 to 310 K) emit most strongly near what wavelength?

About 9 to 10 µm, which is why thermal cameras work in the 8 to 14 µm range.

Near what wavelength does a wildfire (about 1000 K) emit most strongly?

About 3 µm (2898 / 1000 ≈ 2.9 µm), at the border of the SWIR and mid-wave infrared.

GOES ABI is the imager on NOAA's geostationary weather satellites. What is its 3.9 µm "shortwave window" band mainly used to detect?

Fire hot spots, because hot fires emit strongly near 3 to 4 µm.

Which spectral region is best for spotting active fires from space?

Mid-wave infrared near 4 µm, such as the GOES ABI 3.9 µm band (answer keys often just say "thermal infrared").

Why do satellites detect active fires with a band near 4 µm (such as the GOES ABI 3.9 µm band)?

Fires (about 800 to 1200 K) peak near 3 µm, so their 4 µm radiance is huge compared with ground near 300 K.

On a hot, dry, windy day, a thermal infrared image shows a few small spots far hotter than normal daytime heating could make them. What are they most likely?

Active fires (fire hot spots).

MODIS (the main imager on NASA's Terra and Aqua satellites) measures sea surface temperature (SST) with bands near 4 µm and 11 µm. For a sea surface near 300 K (peak about 9.7 µm), where do those bands sit relative to the peak?

4 µm is on the short-wavelength side of the peak, 11 µm just past it on the long side.

Why is a 4 µm band more sensitive to small temperature changes than an 11 µm band when viewing surfaces near 300 K?

4 µm is on the steep short-wavelength side of the Planck curve, where radiance changes much faster with temperature.

Why is MODIS's 4 µm sea surface temperature band used only at night?

By day, reflected sunlight adds to the 3 to 5 µm signal and contaminates it.

Can your eyes see a 3000 K blackbody, even though its peak is near 1 µm in the NIR?

Yes. Its short-wavelength tail still emits plenty of visible red-orange light, like an incandescent filament.

A very cold planet (about 73 K) emits most strongly in what region, at roughly what wavelength?

Far infrared, about 40 µm (2898 / 73 = 39.7 µm, not nm).

Why would you pick a wavelength near a target's Wien peak to detect subtle changes in its emitted radiation?

Emission is largest there, so variations produce the biggest signal.

If Earth warms by 2 K from 288 K, does its emission peak shift much?

No, only about 0.07 µm shorter, since Δλ/λ ≈ -ΔT/T (about 0.7%).

Why is incoming solar radiation called shortwave and Earth's outgoing radiation longwave?

By Wien's law the Sun (about 5800 K) peaks near 0.5 µm, while Earth (about 255 to 288 K) peaks near 10 µm.

Roughly what wavelength ranges count as "shortwave" (solar) and "longwave" (terrestrial) radiation?

Shortwave about 0.2 to 4 µm, longwave about 4 to 100 µm. The two barely overlap.

Why does the radiation a satellite sees switch from mostly reflected sunlight to mostly Earth's own emission around 3 to 5 µm?

Reflected sunlight fades with wavelength while Earth's own emission rises, and the two are about equal near 3 to 5 µm.

Why does the near-separation of the solar and terrestrial spectra matter for the greenhouse effect?

Gases like CO₂ and H₂O can let most sunlight through while absorbing outgoing infrared.

True or false: at radiative equilibrium, Earth emits at the same wavelengths at which it absorbs sunlight.

False. Equilibrium means equal energy in and out, not equal wavelengths (in as shortwave, out as longwave).

Roughly how is the Sun's output split among UV, visible and infrared at the top of the atmosphere?

About half infrared, about 40 to 45% visible, and under 10% ultraviolet.

State the Stefan-Boltzmann law.

Power emitted per unit area M = εσT⁴, so emission is proportional to the fourth power of absolute temperature.

Which law says total emitted radiation is proportional to T⁴, as opposed to Wien's, Planck's, or the Rayleigh-Jeans law?

Stefan-Boltzmann. Wien gives the peak wavelength, Planck the full spectrum, Rayleigh-Jeans the long-wavelength approximation.

What is the value of the Stefan-Boltzmann constant σ?

5.67 × 10⁻⁸ W m⁻² K⁻⁴.

A multiple-choice answer for the Stefan-Boltzmann constant reads "2.898 × 10⁻³ m·K". Which constant is that really?

Wien's constant (σ is 5.67 × 10⁻⁸ W m⁻² K⁻⁴).

In M = σT⁴, what does M stand for, and in what units?

Radiant exitance (emittance), the power emitted per unit area, in W/m².

How is the Stefan-Boltzmann law related to the Planck function?

Integrating (summing) the Planck function over all wavelengths gives the total emission σT⁴.

What does Wien's law tell you about a blackbody, and what does the Stefan-Boltzmann law tell you?

Wien gives WHERE its spectrum peaks (λmax = b/T). Stefan-Boltzmann gives HOW MUCH it emits in total (σT⁴).

If a blackbody's absolute temperature doubles, by what factor does its total emitted energy change?

It multiplies by 16 (2⁴).

If an object's absolute temperature rises by 1%, by about what percentage does its blackbody emission rise?

About 4%, since a small fractional change in T⁴ is four times the fractional change in T.

Two blackbodies have the same size, but one emits 16 times less power. How do their temperatures compare?

The weaker one has half the absolute temperature, since T scales as the fourth root of power.

When comparing the total power emitted by two blackbodies, what must you include besides temperature?

Surface area: P = εσAT⁴, so divide out the area ratio before taking the fourth root.

About how much does Earth's surface (about 288 K, treated as a blackbody) emit per square meter?

About 390 W/m².