Thursday, 26 February 2015

The Uncertainty Principle

The position and momentum of a particle cannot be simultaneously measured with arbitrarily high precision. There is a minimum for the product of the uncertainties of these two measurements. There is likewise a minimum for the product of the uncertainties of the energy and time.

This is not a statement about the inaccuracy of measurement instruments, nor a reflection on the quality of experimental methods; it arises from the wave properties inherent in the quantum mechanical description of nature. Even with perfect instruments and technique, the uncertainty is inherent in the nature of things.

Graphical interpretation of uncertainty principle

Index

Uncertainty principle concepts
 
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Uncertainty Principle

Important steps on the way to understanding the uncertainty principle are wave-particle duality and the DeBroglie hypothesis. As you proceed downward in size to atomic dimensions, it is no longer valid to consider a particle like a hard sphere, because the smaller the dimension, the more wave-like it becomes. It no longer makes sense to say that you have precisely determined both the position and momentum of such a particle. When you say that the electron acts as a wave, then the wave is the quantum mechanical wavefunction and it is therefore related to the probability of finding the electron at any point in space. A perfect sinewave for the electron wave spreads that probability throughout all of space, and the "position" of the electron is completely uncertain.

DeBroglie wavelength

Forms of uncertainty principle

Application example: required energy to confine particles
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Particle Confinement

The uncertainty principle contains implications about the energy that would be required to contain a particle within a given volume. The energy required to contain particles comes from the fundamental forces, and in particular the electromagnetic force provides the attraction necessary to contain electrons within the atom, and the strong nuclear force provides the attraction necessary to contain particles within the nucleus. But Planck's constant, appearing in the uncertainty principle, determines the size of the confinement that can be produced by these forces. Another way of saying it is that the strengths of the nuclear and electromagnetic forces along with the constraint embodied in the value of Planck's constant determine the scales of the atom and the nucleus.
The following very approximate calculation serves to give an order of magnitude for the energies required to contain particles.

Show calculation

Uncertainty principle

Compare to particle in box.

More detailed treatment of 3-D box

Energies in electron volts (eV)
Application example: required energy to confine particles
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Confinement Calculation


If you examine this calculation in detail, you will note that a gross approximation was made in the relationship Δp = h/Δx. This was done to get a qualitative relationship that shows the role of Planck's constant in the relationship between Δx and Δp and thus the role of h in determining the energy of confinement. The other reason for doing it was to get an electron confinement energy close to what is observed in nature for comparison with the energy for confining an electron in the nucleus. If you actually use the limiting case allowed by the uncertainty principle, Δp = hbar/2Δx, the confinement energy you get for the electron in the atom is only 0.06 eV. This is because this approach only confines the electron in one dimension, leaving it unconfined in the other directions. For a more realistic atom you would need to confine it in the other directions as well. A better approximation can be obtained from the three-dimensional particle-in-a-box approach, but to precisely calculate the confinement energy requires the Shrodinger equation (see hydrogen atom calculation).

Confinement discussion

Uncertainty principle

Calculation for 3-D box

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Wavefunction Contexts

Thursday, 19 February 2015

Arthropods Made Easy The Phylum Arthropoda

Arthropods Made Easy
The Phylum Arthropoda


Phylum Arthopoda Review


1. What are some examples of arthropods?

Ants, flies, cockroaches, shrimps, crabs, spiders and scorpions are examples of arthropods.

Phylum Arthropoda - Image Diversity: arthropods



2. What are the classes into which the phylum Arthropoda is divided? What are the three main ones and some of their representative species?
The three main classes of arthropods are: insects (cockroachs, ants, flies, bees, beetles, butterflies), crustaceans (crabs, lobsters, shrimps, barnacles) and arachnids (scorpions, spiders, mites). Other classes are onychophorans (velvet worms), diplopods (millipedes) and chilopods (centipedes).




3. What are the main morphological features of arthropods?
Arthropods present three distinguishing features: they are metameric beings (segmented body), they have an exoskeleton made of chitin and they present articulated limbs.

Phylum Arthropoda - Image Diversity: arthropod structure



4. Concerning germ layers and the presence of coelom how are arthropods characterized?
Arthropods are triploblastic (they have three germ layers) and coelomate beings.




5. Considering the presence of segmentation (metameres) in their body to which other already studied phylum are arthropods proximal?
Considering their metameric feature arthropods are proximal to annelids that also have segmented bodies. In the embryonic development of some arthropods there are fusions of metameres forming structures like, for example, the cephalothorax of arachnids.

Phylum Arthropoda - Image Diversity: athropod cephalothorax



6. What is the external rigid carapace of arthropods called? Of which substance is it made? Which type of organic molecule is that substance?
The external carapace of arthropods is called exoskeleton. The arthropod exoskeleton is made of chitin, a nitrogen-containing polysaccharide.

Phylum Arthropoda - Image Diversity: exoskeleton



7. How do arthropods grow?
Due to the presence of exoskeleton the growth of an arthropod is periodical. During the growth period the animal loses the exoskeleton, grows and develops a new exoskeleton. This process is named ecdysis, or molting.

Phylum Arthropoda - Image Diversity: ecdysis



8. How does the presence of exoskeleton explain the general small size of arthropods?
Since they have exoskeleton and periodic ecdysis, the growth of arthropods is limited to avoid the animal becoming vulnerable to environmental harm. There are however some arthropod species with relatively large-sized individuals, like “giant” cockroaches, crabs and spiders.




9. How can the features of the arthropod exoskeleton explain the terrestrial adaptation of some species of the phylum?
In the arthropod exoskeleton there is a layer of wax which is impermeable. This feature was fundamental for primitive arthropods from the sea to survive on dry land without losing excessive water to the environment.




10. What is the type of digestive system present in beings of the phylum Arthropoda? Are these animals protostomes or deuterostomes?
The digestive tube of arthropods is complete, containing mouth and anus. Arthropods are protostome animals, i.e., in their embryonic development the blastopore originates the mouth.




11. How is the extracorporeal digestion associated to predation in arachnids?
Arachnids can inoculate poison to paralyze or kill their preys using structures called chelicerae. The prey is partially digested outside the body of the arachnid by digestive enzymes inoculated together with the venom or injected posteriorly. After this extracorporeal digestion the food is ingested and gains the digestive tube of the predator where the extracellular digestion continues.




12. Which organs or respiratory adaptations do aquatic and terrestrial arthropods respectively present?
In crustaceans, typical aquatic beings, there are richly vascularized gills that make contact with water and permit gas exchange. In terrestrial insects the respiration is tracheal and gases flow inside small tubes that connect the animal external surface and ramify to tissues and cells without the participation of blood. In arachnids, besides the tracheal respiration, book lungs (thin folds resembling leaves in a book) may also exist.

Phylum Arthropoda - Image Diversity: crustacean respiratory system insect respiratory system arachnid respiratory system



13. In arthropods why isn't gas exchange done through cutaneous diffusion?
In arthropods the impermeability of the exoskeleton makes the passage of gases difficult. In addition the new methods of respiration present in arthropods were preserved by evolution because they were more efficient for those animals.




14. What is the type of circulatory system present in arthropods? Do these animals have heart and respiratory pigments?
In arthropods the respiratory system is open (lacunar). Blood, also known as hemolymph, is pumped by a heart and falls into cavities (lacunas) irrigating and draining tissues.

All arthropods have a heart. Crustaceans and arachnids have respiratory pigments. Most insects do not have respiratory pigments since their blood does not carry gases (in them gases reach tissues and cells through tracheal structures). However, some few insects do have respiratory pigments, hemoglobin (contribution from Jacob Campbell).




15. What are respiratory pigments? What is the respiratory pigment present in some arthropods? Which is the analogous molecule in humans?
Respiratory pigments are molecules able to carry oxygen and other respiratory gases present in circulatory fluids.

In crustaceans and in arachnids hemocyanin is the respiratory pigment. In humans the analogous pigment is hemoglobin.




16. How is the respiratory system of insects (with its independence between circulation and respiration) related to the motor agility of some species of this arthropod class?
Even having low speed and low pressure circulatory system, since it is a lacunar (open) circulatory system, insects perform extremely fast and exhaustive movements with their muscle fibers, like wing beating. This is possible because in these animals the respiration is independent from the open circulation. Gas exchange is done with great speed and efficiency by the tracheal system that puts cells in direct contact with air. Muscles can then work fast and hard.




17. How are the excretory systems of the three main arthropod classes constituted?
In crustaceans a pair of excretory organs called green glands exists. The green glands collect residuals from the blood and other parts of the body. They are connected by ducts to excretory pores located under the base of the antennae and these pores release the excretions outside.

In insects small structures called malpighian tubules gather wastes from the blood and throw them into excretory ducts that open in the intestine. In these animals excretions are eliminated together with feces.

In arachnids, besides malpighian tubules, there are coxal glands located in the cephalothorax near the limbs that also participate in excretion.

Phylum Arthropoda - Image Diversity: arthropod excretory system



18. What are the noteworthy features of the nervous system of arthropods?
In arthropods the nervous system has more sophisticated sensory receptors with well-advanced cephalization. In the anterior region of the body there is a fusion of ganglia forming a brain connected to two ventral ganglial chains having motor and sensory nerves.

The boosted development of the sensory system of arthropods provides more adaptive possibilities for these animals to explore many different environments.

Phylum Arthropoda - Image Diversity: arthropod nervous system



19. What are compound eyes?
Arthropods have compound eyes made of several visual units called ommatidia. Each ommatidium transmits visual information through the optic nerve to the brain, which interprets the image. Because they are round and numerous, these ommatidia, whose external surfaces point in different directions creating independent images, cause arthropod eyes have a large visual field, larger than the visual field of vertebrates. Some insects have one or more simple eye besides their pair of compound eyes.

Phylum Arthropoda - Image Diversity: compound eyes



20. How is arthropod reproduction characterized?
Reproduction in beings of the phylum Arthropoda is sexual, with larval stage in some insects and crustaceans (arachnids present only direct development).




21. What are the types of fecundation that occur in arthropods? What is the predominant type?
In arthropods there are species having external fecundation and other species having internal fecundation. Internal fecundation is predominant.




22. How is fecundation done in insects (external or internal)? Is there copulation between insects?
Fecundation in insects is internal, with copulation.




23. How are the main classes of arthropods classified according to the presence of larval stage in their embryonic development?
In crustaceans there are species with direct and others with indirect development. In insects there are species without larval stage (ametabolic insects), others undergoing indirect development beginning with an egg stage followed by a nymph stage (hemimetabolic insects) and others with indirect development beginning with the larval stage (holometabolic insects).

The transformation of a larva into an adult individual is called metamorphosis. Hemimetabolic insects undergo incomplete metamorphosis while holometabolic insects undergo complete metamorphosis.

Phylum Arthropoda - Image Diversity: metamorphosis



24. What are nymph and imago?
Nymphs are larvae of hemimetabolic insects (like grasshoppers). They are very similar to the adult insect although smaller. In holometabolic insects (like butterflies) the larva makes a cocoon (chrysalis, pupa) where it lives until emerging into the adult form. Imago is the name given to the adult form of insects with indirect development.




25. Is the stage when an insect larva is within a cocoon a stage of total biological inactivity?
The period when the larva is within its cocoon is a time of intense biological activity since the larva is being transformed into an adult animal.




26. How are the three main arthropod classes characterized according to the presence of wings?
Crustaceans and arachnids do not have wings. Most insects have wings.




27. Most insects have wings. Which is the other animal phylum that contains creatures with analogous organs?
Besides the phylum Arthropoda another animal phylum with flying creatures is the chordate phylum, birds and chiropterans mammals (bats) have wings. In the past some reptiles that possibly originated the aves had wings too. There are also amphibians and fishes that jump high exploring the aerial environment.




28. How are the three main arthropod classes characterized according to the presence of antennae?
Crustaceans have two pairs of antennae; insects have one pair; arachnids do not have antennae.




29. How are the three main arthropod classes characterized according to the body division?
In crustaceans and arachnids the head is fused with the thorax forming the cephalothorax. Their body thus is divided into cephalothorax and abdomen.

In insects there are head, thorax and abdomen.




30. How are the three main arthropod classes characterized according to the number of limbs?
Most crustaceans have five pairs of limbs. Insects have three pairs and arachnids present four pairs of limbs.




31. Which arthropod class is the most diversified animal group of the planet? How can this evolutionary success be explained?
The insects are the animal group with most diversity of species. Almost 750000 insect species are known, about 55% of the total already cataloged species of living beings (compare with mammals, with no more than 4000 known species). It is calculated however that the number of unknown species of insects may be over 2 million. The insect population on the planet is estimated to be more than 10 quintillion (1000000000000000000) individuals.

The great evolutionary success of insects is due to factors such as: small size and alimentary diversity, making possible the exploration of numerous different ecological niches; wings that provided more geographic spread; the tracheal respiration that gave them motor agility; high reproductive rates with production of great numbers of descendants.




32. What are some examples of beings of the phylum Arthropoda that present a high level of behavioral sophistication?
Insects like some species of bees, wasps, ants and termites form societies that include hierarchy and job division among members. Spiders build sophisticated external structures, webs, mainly to serve as a trap for capturing prey. Another example is the communication mechanism in some bees known as the bee dance by which an individual signal to others information about the spatial position of flower fields and other nectar sources.




33. Arthropod identity card. How are arthropods characterized according to examples of representing beings, basic morphology, type of symmetry, germ layers and coelom, digestive system, respiratory system, circulatory system, excretory system, nervous system and types of reproduction?
Examples of representing beings: cockroaches, flies, crabs, lobsters, shrimps, spiders, scorpions, mites. Basic morphology: segmented body (metameric), articulated limbs, chitinous exoskeleton, periodic ecdysis. Type of symmetry: bilateral. Germ layers and coelom: triploblastics, coelomates. Digestive system: complete. Respiratory system: tracheal in insects, branchial in crustaceans, tracheal and book lungs in arachnids. Circulatory system: open, hemocyanin in crustaceans and arachnids. Excretory system: malpighian tubules in insects, green glands in crustaceans, malpighian tubules and coxal glands in arachnids. Nervous system: ganglial. Types of reproduction: sexual, with or without larval stage in insects and crustaceans, metamorphosis in some insects, no larval stage in arachnids.