﻿ Light | visible EME spectrum | CalQlata

# Light

An intriguing question!

The sun's surface temperature is ≈5778K (yellow);
λ = 6.273466E-07 m     ƒ = 4.778737E+14 /s     A = 3.039921E-10 m     EME = 3.794634E-19 J
putting it in the middle of the visible (to us humans) range of the electro-magnetic energy (EME) spectrum (Fig 4)

Fig 1. The Colour of a Near Star

However;
the colour of a tungsten filament is bright yellow-white at a temperature of only 2884K;
λ = 1.779092E-06 m     ƒ = 1.685087E+14 /s     A = 6.090545E-10 m     EME = 1.893982E-19 J
which should put it outside the visible range of the EME spectrum.

How can this be?

## White-Light

EME comprising red, green and blue (Fig 4) will together appear white to our eyes, but only if the emissions are synchronous (running together along the same path).

colour (Fig 4) λ (m) ƒ (/s) A (m) EME (J) (K)
red 7.56E-07 3.96E+14 3.44E-10 3.35E-19 5400
green 5.38E-07 5.57E+14 2.74E-10 4.2E-19 6400
blue 4.6E-07 6.51E+14 2.47E-10 4.66E-19 7100

In other words; combining all the colours of the visible spectrum in the same synchronous path will appear white to an observer.

## Starlight

A star's atmosphere is almost entirely hydrogen and helium, the leftover elements from total fissionable disintegration. This means that all of the proton-electron pairs at its surface are orbiting in the same Shell (shell-1), and at similar velocities, radiating EME at similar energy levels (≈3.8E-19J) and therefore similar colours; various shades of yellow.
The surface of stars cooler than our sun will look a little darker, orange (or even red), and hotter stars will look brighter, green (or even blue) when viewed close-up.

Like all stars, our sun comprises all the elements, the proton-electron pairs of which, radiate EME at temperatures ranging from 5778K (@ its surface) to Ṯₙ (in its core). It appears yellow to us because its relative size ensures that most of the radiated EME reaching us is asynchronous and the sun's atmospheric temperature (5778K) is dominant at its surface.
A star appears white to a distant observer because virtually all its radiated EME, including its core EME, is synchronous due to its apparent size (Fig 2).

Fig 2. The Colour of a Distant Star

In other words, the larger a star’s visibility, the more apparent its surface colour will be to an observer.
Moreover, our sunlight (visible EME) is generated at its surface temperature (5778K), but by the time it reaches us here on earth, its intensity will have diminished by between 44704.56 and 47794.87 (dependent upon the time of year). This means that whilst the sun's yellow EME will still appear yellow on earth, its heat will be about 46000 times lower due to its much-reduced intensity.

## Filament Light

But what about the tungsten filament?
As stated above, when activated, a tungsten filament is bright (yellow-white) at just 2884K, but this doesn't fit the electro-magnetic spectrum. It should be outside the visible range (infra-red).

The wavelength of the EME radiated by our sun ranges from 1.77E-14 m at the core where its matter is gaseous to 6.27E-07 m at the atmospheric surface where the atoms are also gaseous. However, because the sun comprises all the elements, its atoms contain proton-electron pairs radiating EME at all temperatures; for example, the outermost proton-electron pairs in a silicon atom at a measured temperature of 7100 K will be radiating EME at just 1014 K. So, the EME radiated by our sun covers all EME from infra-red to gamma. It therefore radiates all the visible colours, as can be seen in rainbows here on earth. And is the reason we can convert sunlight to white-light through a prism.

Fig 3. Internal Temperatures

A similar situation applies to our earth, but at much lower temperatures; for example, its core temperature is only around 6000 K. Whilst much of its mantle matter is also gaseous, it is contained in much cooler viscous matter in its crust. Therefore, very little of the EME radiated by the earth at its surface - if we exclude that reflected by sunlight - is within the visible range. This is why the earth's surface looks black in outer-space when viewed from the opposite side of the sun's radiation.

A light-bulb filament is very small, but there are still 88500 atoms from its core to its surface; at which its measured temperature is 2884 K. Its core temperature, however, is much higher (>7000 K; blue). Whilst tungsten at less than 6200 K (gas-transition temperature) is strong enough to contain the gaseous core atoms, the nominal radial distance from core to surface allows all of its EME to exit the filament. And because it all originates from the same core atoms, it all exits synchronously, making it white in colour. If the filament is very small, the white-light will be bright. If the filament is larger, its radiated EME will be cooler; yellow-white.

In other words, whilst the measured filament temperature is outside the visible EME range, most of its inner proton-electron pairs are radiating EME synchronously in the visible range. This is why we can see a light-bulb filament at only 2884 K.

Fig 4. The Visible Range of the Electro-Magnetic Spectrum

### Further Reading

You will find further reading on this subject in reference publications(68 to 74)

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