exchemist

Your "definition" of momentum is wrong and you are using the wrong formula. According to special relativity, E=mc² is not applicable to a photon. I went over this in post 11 of this thread.

This sheds some light on your question: https://knowyourdna.com/skin-color-genes/

Exactly. But I can elaborate. Firstly, there is no way to define "perfection" in this context. What can it mean? Secondly, there will always be sub-optimal features of any creature, however it has been bred. You can breed for one - questionable and highly subjective - ideal of physical beauty but end up with a creature prone to disease, or with a horrible temperament, or with allergies, or poor digestion etc. When you breed to optimise one aspect you inevitably sacrifice others.

No.

No idea. I am not an expert on pesticide chemistry.

Ah but that’s in the LM, when they were actually on the moon. What about the command module, which was less stressful and more comfortable? https://space.stackexchange.com/questions/35869/which-module-had-more-comfort-in-terms-of-living-space-the-lunar-module-or-th

In the case of IPA, if it is just the pure alcohol not much is going to go wrong with it over time. If there is any long-term oxidation it might generate a bit of acetone, that's all. The main risk would probably be degeneration of the container, if it is plastic rather than glass. Pesticides may however be a different kettle of fish, being more complex molecules that may possibly break down or oxidise in a variety of ways. So for those I would probably not want to exceed the stated shelf life too much, not by more than a year or two at most.

No, you have made that bit up about the amount of disturbance being associated with mass.

Yes, there is energy in fields, for example in an energised electromagnet. With photons, the “medium” is the electric and magnetic fields. A photon is a travelling disturbance in those fields.

No, a wave is not energy. A wave is a disturbance in a medium that has energy. A wave has many properties, of which energy is just one. If you are perhaps thinking of E=mc² , you need to be aware that that is a special case of Einstein's more general expression relating energy to mass and momentum, which is : E² = (mc²)² +(pc)² . p in this expression is momentum. For objects at rest relative to the observer, p=0, so it reduces to the familiar E=mc². But for light, which has no rest mass, m=o, so the expression reduces instead to E=pc. It is this that governs the energy of a photon, not E=mc². In fact, if you apply to this de Broglie's relation from quantum theory, which relates momentum to wavelength: p=h/λ (h is Planck's constant), you get something interesting. For any wave, the speed, c, frequency ν, and wavelength, λ, are related by c = νλ. So you can write 1/λ = ν/c. de Broglie's expression then becomes p = hν/c, and so E=pc becomes E=hν. This is Planck's famous equation for the energy of electromagnetic radiation.

This looks to me like quite an advanced applied mathematics question and as such is beyond me, I'm afraid. I started wondering about catenaries for a moment, but I don't know what I'm talking about. I think @studiot may be a mathematician. I wonder if he has any ideas.

I can't help you with the maths, but physically I think it may not be correct to assume that the surface of the droplet becomes vertical when the maximum mass it can support is reached. You have a constant surface tension (of 70 dynes/cm or so) and there will come a point at which the weight of the water exceeds the force from the vertical component of this tension. But it is not immediately clear what maximum angle from horizontal the surface will attain when that point is reached. It could well be that the weight becomes too much when the angle is only π/4, or some other angle. I think this has to be calculated.

Any wave carries energy. A wave is just a travelling disturbance in some medium. It takes energy to displace the medium away from its equilibrium state, and that is the energy carried by the wave. A wave can't be said to have any particular mass. A photon is a travelling disturbance in the electric and magnetic fields. Mass does not need to come into it.

Starch is a term for polysaccharide polymers, assembled from glucose monomer units. However there can be differences in molecular weight and in degrees of chain branching, not to mention grain size and possibly other physical characteristics, depending on the source.

My sentiments exactly, Doctor. I hope to God @toucana is right about Trump being behind bars before the election. If the US gets taken over by an authoritarian personality cult, we get worryingly close to the power blocs of Orwell’s 1984, turbocharged by the surveillance state, internet disinformation and AI.

Well, it starts to get interesting. I did not find any instructions for demonstrating how to do this using lycopodium spores but instead came across this amateur site: http://www.microscopy-uk.org.uk/mag/indexmag.html?http://www.microscopy-uk.org.uk/mag/artoct20/ms-brownian.html which seems to claim the grains are too big to show Brownian motion themselves and it is only when they burst and release their contents that there are particles small enough to demonstrate the effect. This site also says the hydrophobic properties of lycopodium spores are due to air trapped by hairs on their surface. If so, when they burst, this would not apply to their contents - which might then be able to disperse in the body of the liquid. So maybe we are getting somewhere.

This does not seem to address my point. I suppose one advantage of the particles clinging to the glass surface would be that they all stay in one plane and thus can be easily kept in focus when examined with the microscope. I would have thought their motion might be inhibited somewhat by contact with the glass, but apparently it is not enough to prevent the demonstration from working. I suppose if they are hydrophobic they will probably not be strongly stuck to the glass either, since that too is a polar medium. Perhaps what I need to do is find some detailed instructions for how to set this demonstration up, and see what they say about it.

Yeah but I'm not questioning whether or not it is used to show Brownian motion. Evidently it is. It is just that my previous understanding of the demonstration, that the particles were in the body of the liquid and being buffeted in all directions by water molecules, can't be correct. They must be clinging to the glass and sliding around in 2 dimensions only.

I've given you the example of the towels my wife bought, which do exactly this. They came from a mid-price fabric and furnishing store in France (Bouchara, in Vannes, I think), so were respectable quality but not top notch. So yes it can happen. This is why you are always advised to wash dark coloured garments together, separately from light ones. You can wash them with jeans, dark socks and underwear, dark blue or dark green shirts and trousers, etc. and there will be no effect. So just do that, like everybody else, and get on with life.

I don't know anything about clothing brands, but all dyes can run if not fixed well. Black, being so dark, will be particularly obvious when it happens. I have some maroon coloured bath towels (a slightly mad choice of colour by my late dear wife, hem hem) which still run a bit after 15 years, so I have to wash them only with other reddish items. But I also have a (Barbour) shirt with dark blue, green and cream colours in it, that is absolutely fine. Clearly, the manufacturer had the wit to realise that putting these colours together required the dyes to be well fixed, to avoid the shirt being wrecked the first time the customer washes it. Barbour is a good - and expensive - brand however. I suspect your items may not be the best quality if the black runs. However the good-ish news is that black, unlike say blue or red, will just make other items in your wash a bit grey, rather than changing their colour in an obvious and potentially more damaging way. It will probably be best to wash them with other dark clothes and not at a high temperature. There's a bit of explanation here from a detergent manufacturer, which may shed some light on the issue: https://www.persil.com/uk/laundry/laundry-tips/washing-tips/knew-one-colour-runs-wash-another.html

Thanks - something I did not know. But that raises a question in my mind about its use to demonstrate Brownian motion. My understanding is this is done in a water droplet on a microscope slide. But if the grains are hydrophobic, then presumably they will not be in the bulk liquid but clinging to the glass of the slide and being nudged this way and that, along the surface of the glass. Is that your understanding? Or is a surfactant used to to get them to disperse into the water?

Oh great!

Why do you say lycopodium powder grains are hydrophobic?

Sure. What I had in mind though is that at each interaction there is one value made concrete out of a range of probabilities and this value goes on to set the conditions for the thing interacted with, which at its next interaction in turn makes concrete one value out of a range, etc etc. So at the end of the chain of interactions the outcomes are not determined exactly by the starting conditions.

Well both are indeed false. 1) There is no such thing as a "hydrophobic force". For a non-polar molecule to dissolve into water, it has to get between the water molecules. There will be attractive London forces between water molecules and the non-polar molecule, but its presence between water molecules will reduce their mutual hydrogen bonding and thus raise the energy of the solution, so it is energetically unfavourable - and will only happen to a slight extent. (Dissolution is still favoured entropically, so the free energy change won't be determined purely by the enthalpy change. The influence of entropy will be greater as the temperature goes up: ΔG = ΔH-TΔS. ) So there is no "repulsion" of any kind: it's just a reduction in net attractive force. 2) I had actually forgotten this 🙂, but D and L stereoisomers are a naming convention, relating chiral molecules to the enantiomers of glyceraldehyde, i.e. to the way those rotate the plane of polarised light. It does not mean and given D or L stereoisomer will rotate polarised light in a particular way. More here: https://chem.libretexts.org/Courses/Purdue/Purdue%3A_Chem_26200%3A_Organic_Chemistry_II_(Wenthold)/Chapter_22._Carbohydrates/22.03%3A_The_D_and_L_Notation