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A Brocken spectre is a visual effect in cloud or mist where a person sees their shadow with colored concentric rings centered around the head. It occurs at high elevations like mountain peaks when sun directly behind an observer casts their shadow on cloud or mist below. The colored rings, called a glory, arise from backscattering of sunlight that has undergone multiple internal reflections within tiny water droplets in the cloud. It was called a spectre because optical illusions often make the shadow appear oversized. The name Brocken comes from the highest peak in Germany’s Harz mountains, one of the places where the phenomenon has previously been observed.

Orbitals, the regions around an atom’s nucleus likely to be occupied by electrons, are grouped into subshells identified by energy level (1, 2, 3, 4 and so on) and orbital shape (s, p, d, and f). The 3d subshell contains five orbitals, each able to hold up to 2 electrons, a total of 10 electrons if all filled. Transition metals have stable ions with only a partially filled 3d subshell, and five degenerate d-orbitals, meaning they all have the same energy. When a transition metal ion bonds with a ligand to form a transition metal complex, electron repulsion causes the d-orbitals to become non-degenerate, separating into two different energy levels. As the subshell is not full, electrons from the lower energy level 3d orbitals can jump to the higher energy 3d orbitals by absorbing visible light, with the energy difference between the levels determining the wavelength, and hence the color, of light absorbed. Visible light wavelengths not absorbed give the transition metal complexes their distinctive colors.

Most liquids contract when cooled, getting denser until they freeze into a solid. Their moving molecules lose kinetic energy, slowing them down, so they become prone to the attractive forces of nearby molecules drawing them closer together. Water exhibits this normal behavior down to 4 degrees Celsius (or 39.2 degrees Fahrenheit) where its density reaches a peak, but cooling actually sees it start to expand again. From 4°C, whether you cool or heat it, water expands. This anomalous behavior occurs because as water molecules come closer together with cooling, they are increasingly inclined to form hydrogen bonds between the oxygen atom of one molecule and the hydrogen atom of a neighboring molecule. This starts to form structured hydrogen-bonded clusters of water molecules which actually begins to increase the distance between them, reversing the increasing density trend observed up to that point. Further cooling to freezing ultimately forms an orderly crystalline lattice of solid ice which is actually less dense than its liquid water state. 4°C is the point above which the normal effects of thermal kinetic expansion prevail over water’s tendency to form hydrogen bonds.

Glow sticks contain hydrogen peroxide solution and a separate sealed glass tube of diphenyl oxalate ester solution mixed with a fluorescent dye. Bending the glowstick breaks the inner glass tube, mixing the two solutions, and starts a chemical reaction. The reaction makes 1,2-dioxetanedione, a cyclic dimer of carbon dioxide, which rapidly decomposes to carbon dioxide, releasing energy that excites electrons in the dye molecules. As those electrons fall back to a stable state, the dye molecules release energy as photons of light. This is called chemiluminescence and the dye molecule used governs the light wavelength emitted, and hence the glow stick color.

Sound travels almost 3 times as fast in helium gas than in normal air because helium is less dense. Contrary to common perception, helium does not make the voice high-pitched, because voice pitch is determined by the vibration frequency of the vocal chords generating the sound. So, while the fundamental pitch of the voice is actually unchanged, what helium does is change the timbre of the vocal sound compared to speech produced in normal air. The vocal tract, nasal cavities and mouth create acoustic resonances, known as formants, from the sound generated by the vocal cords. Because the sound waves move faster in helium-laden breath, the stronger resonances shift towards higher frequencies and drastically change the overall tone quality of the emitted voice.

An ideal gas is a scientific concept underpinning the Ideal Gas Law, of a theoretical gas with strictly defined properties for the purpose of understanding, predicting, and explaining the behavior of real gases under different conditions of temperature, pressure and volume. In an ideal gas: Molecules are spheres which collide elastically with each other and the container walls, so the total kinetic energy after a collision remains the same as before. There are no long-range forces of attraction or repulsion between molecules. Individual molecules occupy no volume, so a molecule’s size is ignored relative to the volume occupied by the gas as a whole. In reality no real gas exhibits such properties without deviation, but most real gases at room temperature and normal atmospheric pressures behave sufficiently closely that the theoretical model is a useful approximation for scientific study.

A temperature of minus 40 degrees is the same in both Celsius and Fahrenheit. It is the only temperature point on the F and C scales where this occurs.

The light we see from the sun is made up of a rainbow spectrum of colors from red through blue to violet. As light passes through the Earth’s atmosphere, it hits small gas molecules and particles in the air and gets scattered in different directions. This is known as Rayleigh scattering. As blue light has more energy than, say, red light, the blue light component of sunlight is scattered more strongly in the atmosphere. So, what we see when looking up is an excess of the higher energy blue light being scattered compared to other lower energy colors, and hence the sky appears blue.

An ion is an atom or molecule carrying an electrical charge because it has an unequal number of protons and electrons. By convention, protons are considered positively charged, and electrons negative and a net electrical charge results whenever there is more of one than the other. An ion with more protons than electrons carries a net positive charge and is called a cation. Conversely, an anion is a negatively charged ion because it has more electrons than protons.

Most commercial aircraft cabin windows are made of three plastic panes, each separated by a small air gap. The tiny hole at the bottom of the window is a bleed hole through the center pane to equalize the pressure inside the window unit with the cabin air pressure. By design, this ensures it is the outermost window pane bearing the load of the internal cabin air pressure pushing outwards on the window during high altitude flight. Venting through the hole also prevents condensation fogging up the windows.