The densest water originates from low latitudes.

True
False

Answers

Answer 1

False. The densest water is produced at high latitudes where the water is cold and has a high concentration of dissolved salts, causing it to be more dense. This dense water sinks to the ocean floor and spreads to lower latitudes, where it has a significant impact on global ocean circulation.

What is densest water?

The densest water is known as North Atlantic Deep Water, which is the densest and coldest water in the ocean. It is formed in the North Atlantic Ocean near the Labrador Sea and Greenland, where the water is cooled by the atmosphere and becomes denser due to the high concentration of dissolved salts.

Dense water then sinks to the ocean floor and spreads to other parts of the world ocean playing a crucial role in the global ocean circulation system.

North Atlantic Deep Water is one of the most important and well-studied water masses in the ocean, as it has a significant impact on the Earth's climate and weather patterns.

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Related Questions

Why is the Diels Alder reaction reversible at high temperatures?

Answers

As starting materials have a higher entropy than products, all Diels-Alder processes may be reverted to initial diene and dienophile at sufficiently high temperatures.

Cycloaddition reversibility is one of the factors that contribute to endo-selectivity loss. Cycloreversion reactions are particularly common in aromatic dienes (such as furan and anthracene). Retro-Diels-Alder reactions can be utilised to create reactive olefins or other -bonds utilising flash vacuum pyrolysis.

For this purpose, anthracene, 9,10-dimethylanthracene, cyclopentadiene, and dimethylfulvene seem to be particularly suitable. If heated enough, the product of a Diels-Alder reaction can undergo a reverse reaction that recharges the initial konnect and generates a set (which both happen to be cyclopentadiene in this case). The backward (or "retro") reaction seems to be the Diels-Alder reaction.

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Project: Analyzing Chemical Reactions
I need Charts, Graphs, and Data

Answers

A chemical reaction is usually accompanied by easily observed physical effects such as heat and light emission, precipitate formation, gas evolution, or color change.

What is chemical reaction ?

A chemical reaction is a process that converts one or more substances, known as reactants, to one or more different substances, known as products.

A graph can be used to depict the relationship between two values, the dependent and independent variables. A measurable variable whose value is determined by the independent variable.

Graphs and charts condense large amounts of information into simple formats that communicate key points clearly and effectively.

Thus, Physical effects such as heat and light emission, precipitate formation, gas evolution, or color change are typically observed during a chemical reaction.

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Which molecules are bound to hemoglobin when hemoglobin is in the R state? CO2,
3-bisphosphoglycerate Fel2+ oxygen Fe+

Answers

The offered statement states that oxygen atoms are bonded to hemoglobin when it is in the R state.

Do people make up molecules or atoms?

The molecules that make up the human body are incredibly diverse, but they are all combinations of just a few dozen basic constituents: the elements of period 3 that are chemical. However, there are significant differences in each atom's abundance.

What binds molecules collectively?

Chemical bonds, which are required for the existence of chemicals, are the temporary connections that bind compounds together. London dispersion forces and ionic, solid, and hydrogen bonds are examples of chemical bonding.

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Why is ionic bonding considered both inter- and intramolecular bonding? a. lonic bonds are strictly intermolecular forces. b. Ionic bonds are strictly intramolecular bonds. Each lattice is a single large molecule of some substance. c. lonic solids form directly from gases 1 atom at a time. d. Molecules arrange themselves in a grid, and it's hard to tell where one molecule ends and the other begins.

Answers

Ionic bonding considered both inter- and intramolecular bonding because molecules arrange themselves in a grid, and it's hard to tell where one molecule ends and the other begins.

option D

Why is ionic bonding considered both inter- and intramolecular bonding?

Ionic bonding is considered both inter- and intramolecular bonding because it involves the transfer of electrons from one atom to another to form ions, which are held together by electrostatic attraction.

Intramolecular bonding refers to the bonding that occurs within a single molecule, while intermolecular bonding refers to the bonding that occurs between molecules. In the case of ionic bonding, the attraction between ions of opposite charges within a single molecule constitutes intramolecular bonding, while the attraction between the ions of opposite charges in adjacent molecules constitutes intermolecular bonding.

Option (d) is not entirely accurate because the arrangement of ions in an ionic lattice is not based on the formation of individual molecules but rather on the organization of ions in a repeating pattern. However, it is true that the boundaries between individual molecules are not well-defined in an ionic lattice.

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What is the term used to describe breaks in earth'crust by which rokes moves or slide past one another

Answers

The term used to describe breaks in the Earth's crust by which rocks move or slide past one another is "fault." Faults can be caused by tectonic plate movement.

Faults generates stress on the Earth's crust. When the stress becomes too great, the rocks along the fault plane can break and move, resulting in an earthquake. There are different types of faults, including normal faults, reverse faults, and strike-slip faults, depending on the direction of movement between the rocks.

Faults are essential in shaping the Earth's surface, and studying them can help geologists better understand the past and future movements of tectonic plates.

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Can yall help me with this

Answers

Aquifer - B. Stores water in the ground

Reservoir - C. A body of water which is used to store water for human use

Runoff - A. Water that moves across the surface of land into streams or rivers

Transportation - D. The release of water vapor from the leaves of plants

A chemical reaction is carried out in a closed container. The energy absorbed by the chemical reaction is 200 kJ.

How much thermal energy moves inward from the air or the walls of the container?

75 kJ

100 kJ

150 kJ

200 kJ

Answers

The energy absorbed by the chemical reaction is 200 kJ. 200 kJ is the thermal energy that moves inward from the air or the walls of the container. Therefore, the correct option is option D.

What is thermal energy?

Thermal energy is a sort of kinetic energy since it is generated by particle movement. Kinetic energy refers to the energy that an item possesses as a result of its motion. The more the form of heat of a body, the faster its atoms, molecules, or atoms travel.

A chemical reaction is carried out in a closed container. The energy absorbed by the chemical reaction is 200 kJ. 200 kJ is the thermal energy that moves inward from the air or the walls of the container.

Therefore, the correct option is option D.

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You make a solution of a nonvolatile solute with a liquid solvent. Indicate whether each of the following statements is true or false. (a) The freezing point of the solution is higher than that of the pure solvent. (b) The freezing point of the solution is lower than that of the pure solvent. (C) The boiling point of the solution is higher than that of pure solvent. (d) The boiling point of the solution is lower than that of the pure solvent.

Answers

The solution's freezing point is higher than the solvent's pure freezing point. The solution has a boiling point that is greater than a pure solvent.

What happens when you add a nonvolatile solute to a liquid?

The boiling point of a solvent increases and the vapour pressure decreases when a nonvolatile solute is added. A substance that does not readily evaporate is referred to as a nonvolatile solute.

When non-volatile substances are added to a solvent, the vapour pressure is reduced, and the solute particles have an impact on how pure solvent crystals form. According to numerous studies, the amount of solutes dissolved in the solvent directly correlates to the drop in freezing point. The vapour pressure of a non-volatile solute drops when it is dissolved in a volatile solvent.

Therefore, the correct answer is option

(a) The freezing point of the solution is higher than that of the pure solvent.

(C) The boiling point of the solution is higher than that of pure solvent.

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What is the name of the organic compound ch3 ch2 ch2 ch3?

Answers

The name of the organic compound CH₃CH₂CH₂CH₃ is butane.

Butane is an alkane with four carbon atoms and a straight chain. The prefix "but-" indicates four carbon atoms, and the suffix "-ane" indicates that the molecule is an alkane with all single bonds between the carbon atoms.

The molecular formula for butane is C₄H₁₀. Butane is a highly flammable gas at room temperature and pressure, and it is commonly used as a fuel for lighters, camping stoves, and other portable heaters. It is also used as a refrigerant, propellant, and solvent in various industrial applications.

It is a member of the homologous series of alkanes, which have the general formula CnH₂n+2, where n is the number of carbon atoms in the molecule.

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50 gram sample of water at 100 degrees celcius is poured into a 50 gram sample of water at 25 degrees celsius. what will be the final temperature of the water

Answers

The heat released is equal to the heat gained. Hence, the final temperature is 62.5∘ C.

What is temperature gradient?

A temperature gradient is a physical quantity that describes in which direction and at what rate the temperature changes the most rapidly around a particular location. The temperature gradient is a dimensional quantity expressed in units of degrees per unit length. The SI unit is kelvin per meter.

In weather forecast and climate, the differences between the air temperature between between different locations. The planetary surface's absorption of solar light raises the temperature gradient and may cause convection (a major process of cloud formation, often associated with precipitation). Since meteorological fronts are the boundaries between air masses with distinctly different characteristics, the horizontal temperature gradient may reach relatively high values in these areas.

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How many liters of laughing gas
(N₂O) do you have if you have 3.02 x 10^23 molecules of laughing gas at normal conditions?

Answers

The volume of the gas is 11.2 L

What is the mole?

The mole is the standard unit of measurement for amount of substance in the International System of Units (SI). It is defined as the amount of a substance that contains the same number of entities as there are in 12 grams of carbon-12. This number of entities, known as Avogadro's number, is approximately 6.022 x 10^23.

If 1 mole could contain 6.02 * 10^23 molecules

x moles would contain  3.02 x 10^23 molecules

x =  0.5 moles

Then;

1 mole of the gas occupies 22.4 L

0.5 moles of the gas occupies 0.5 * 22.4/1

= 11.2 L

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Given that syn addition of H2H2 occurs from both sides of a trigonal planar double bond, draw allstereoisomers formed when each alkene is treated with Hâ2Hâ2.

Answers

When an alkene is treated with H2H2, the addition can occur from either face of the double bond, resulting in two different stereoisomers.

This is known as syn addition because the two hydrogen atoms are added to the same face of the alkene. The stereoisomers that result from the addition of H2 to an alkene will depend on the specific alkene and the arrangement of its substituents.

For example, when 1,2-dimethylcyclohexene is treated with H2H2, two stereoisomers are formed: (1R,2S) and (1S,2R). These stereoisomers can be differentiated by their molecular configurations, which are determined by the arrangement of the substituents on the cyclohexene ring and the position of the hydrogen atoms on the double bond.

Similarly, other alkenes will give rise to different stereoisomers upon syn addition of H2, depending on the specific alkene and its substituents.

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True or False? imagine an emission spectrum produced by a container of hydrogen gas. changing the amount of hydrogen in the container will change the colors of the lines in the spectrum.

Answers

The given statement "An emission spectrum produced by container of the hydrogen gas. when we changing the amount of hydrogen in the container will change the colors of lines in the spectrum" is true. Because the colors of the lines in the emission spectrum produced by a container of hydrogen gas depend on the energy levels of the hydrogen atoms.

The emission spectrum produced by a container of hydrogen gas contains a series of discrete lines corresponding to the specific wavelengths of light emitted when excited hydrogen atoms release energy. The colors of these lines are determined by the energy differences between the electron energy levels involved in the transitions.

Changing the amount of hydrogen in the container would alter the number of hydrogen atoms that can emit light, and thus, the intensity of the lines in the spectrum. It would not, however, affect the energy differences between the electron energy levels, and therefore, the colors of the lines would remain the same.

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Is Cl2 polar covalent nonpolar covalent or ionic?

Answers

The molecule of chlorine Cl₂ is nonpolar covalent in nature.

A single covalent link holds the two Cl atoms together. The positive Cl atom's nucleus and the covalent bond's negative electron pair are attracted to one another.

Cl₂ molecule of gas is made up of two chlorine element atoms. As a result, Cl₂ won't show metallic boding. Cl₂ must be covalent since an ionic bond can only be formed when a metal and a non-metal come into the contact. As a result, we deduce that the chlorine molecule is non-polar covalent.

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Question: Determine The Product Formed When Each Compound Is Treated With Br_2 And FeBr_3. Drag The Atom Labels To Their Appropriate Positions.

Answers

When m-xylene is brominated with bromine while ferric bromide is present, the product is 1-bromo-2,4-dimethylbenzene.

What products are formed when the following compound is treated with bromine in the presence of [tex]$\mathrm{FeBr}_3$[/tex]?

M-bromonitrobensene is the main product created when nitrobenzene is treated with [tex]$$Br_2[/tex] in the presence of [tex]$\mathrm{FeBr}_3$[/tex].

If [tex]$\mathrm{FeBr}_3$[/tex] or [tex]$$AlBr_3[/tex] are not added to produce the electrophile Br+, benzene will not react with [tex]$$Br_2[/tex] ([tex]$\mathrm{FeCl}_3$[/tex] and [tex]$$AlCl_3[/tex] can also be used, but may contaminate the products with chlorine). There won't be any reaction if the metal chloride is absent, hence there won't be any colour change.

When m-xylene is brominated with bromine while ferric bromide is present, the product is 1-bromo-2,4-dimethylbenzene. Since methyl groups are ortho para directing, the replacement takes place at a site that is ortho to one methyl group and para to another methyl group in this electrophilic aromatic substitution reaction.

The complete question is:

What product are formed when the following compound is treated with [tex]$\mathrm{Br}_2$[/tex] in the presence of [tex]$\mathrm{FeBr}_3$[/tex]?

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According to Dalton’s law of partial pressures the pressure of oxygen in dry air would be

2.12kPa

21.00kPa

21 kPa

21.22 kPa

Answers

The partial pressure of oxygen in the dry air, given the partial pressure of the rest gases is 21.22 KPa (Last option)

How do I determine the partial pressure of oxygen?

From Dalton's law of partial pressure, we understood taht the partial pressure of the gases present in a system is given as follow:

Total pressure = Partial pressure of gas A + Partial pressure of gas B

With the above formula, we can determine the partial pressure of oxygen. Details below:

Partial pressure of nitrogen = 79.11 KPaPartial pressure of carbon dioxide = 0.04 KPaPartial pressure of argon and other gas = 0.95 KPaTotal pressure = 101.32 KPaPartial pressure of oxygen = ?

Total pressure = Partial pressure of nitrogen + Partial pressure of carbon dioxide + Partial pressure of argon and other gas + Partial pressure of oxygen

101.32 = 79.11 + 0.04 + 0.95 + Partial pressure of water vapor

101.32 = 80.1 + Partial pressure of water vapor

Collect like terms

Partial pressure of oxygen = 101.32 - 80.1

Partial pressure of oxgyen = 21.22 KPa

Thus, the partial pressure of oxygen is 21.22 KPa (Last option)

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What is the mass (in grams) of 6.15 × 1025 molecules of carbon dioxide?

Answers

Avogadro's Number and Stoichiometry

To convert between moles and molecules, we can multiply the number of moles by Avogadro's number: [tex]6.02*10^{23}[/tex]

To convert between moles and mass, multiply the moles by the molar mass of the compound.

Solving the Question

We're given:

[tex]6.15*10^{25}[/tex] molecules

Divide this by Avogadro's number:

[tex]\dfrac{6.15*10^{25}}{6.02*10^{23}}\\\\= 102.1594684\hspace{4}mol[/tex]

Multiply by molar mass (44.01 from Chemspider):

[tex]102.1594684*44.01\\=4.5*10^3\hspace{4}g[/tex]

Answer

[tex]4.5*10^3\hspace{4}g[/tex]

Which metal oxide will be reduced by heating with iron?
A calcium oxide
B lead oxide
C magnesium oxide
D zinc oxide

Answers

Answer:

calcium oxide

Explanation:

Correct option is A)

Magnesium metal is an alkaline earth metal. The tendency of these metals is to lose electron. They lose electron and form oxide. Now, they are stable hence it is very difficult for them to again gain that electron. Hence, they are not reduced by normal reducing agents.

How many grams of NaOH are required to produce 9.23 moles of NaCl?

Step-by-step please

Answers

Answer:

369.20 grams of NaOH are required to produce 9.23 moles of NaCl.

Explanation:

To answer this question, we need to know the balanced chemical equation for the reaction between NaOH and HCl, assuming that the reaction takes place in an aqueous solution:

NaOH + HCl → NaCl + H2O

According to this equation, 1 mole of NaOH reacts with 1 mole of HCl to produce 1 mole of NaCl and 1 mole of water.

To calculate the amount of NaOH required to produce 9.23 moles of NaCl, we need to use the mole ratio between NaOH and NaCl from the balanced equation. Since the mole ratio is 1:1, we know that we need 9.23 moles of NaOH to produce 9.23 moles of NaCl.

The molar mass of NaOH is 40.00 g/mol, which means that 1 mole of NaOH weighs 40.00 grams. Therefore, 9.23 moles of NaOH weighs:

9.23 moles x 40.00 g/mol = 369.20 grams of NaOH

So, 369.20 grams of NaOH are required to produce 9.23 moles of NaCl.

Include one paragraph to explain the movement of energy during phase transitions.(solid, liquid gas)

just a quick 4 or 5 sentences about the 3 states of matter you wrote yourself please(i dpnt care how detailed it is)

Answers

The energy movement from solid liquid to gas is always going up and moving faster. A solid is a tight definite shape where the molecules are all stuck in one place and there’s barely energy and movement. The liquid has a more free space since it does not have a definite volume energy moves around quicker. The gas phase would have energy going everywhere Becuase it doesn’t have a definite shape and volume. As temperature goes up the kinetic energy also goes up

What is the generic name of gabapentin?

Answers

The generic name of the gabapentin is the  Neurontin. The Gabapentin is used to treat the epilepsy.

The generic name of the gabapentin and It is also taken for the nerve pain, and which can be caused by the different conditions, it also diabetes and the shingles. The Nerve pain can also be happen after the injury. The Gabapentin is generally used to treat the some types of the nerve pain but it is also classified as the anticonvulsant medicine, but it is not used as the opioid or the painkiller.

Thus, the Neurontin is the generic name of the gabapentin.

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PLEASEEEEEEEE HELP ON THIS

Answers

The answer is 4
m1=5
m2=20
d=5
(5*20) / (5^2)
100 / 25
Equals 4

a solid that forms and settles out of a liquid mixture

Answers

A solid that forms and settles out of a liquid mixture is called suspension /precipitate.

A suspension is a heterogeneous mixture in which some of the particles settle out of the mixture upon standing. The particles in a suspension are far larger than those of a solution, so gravity is able to pull them down out of the dispersion medium (water). Suspensions are considered heterogeneous because the different substances in the mixture will not remain uniformly distributed if they are not actively being mixed.

An example of a suspension would be sand in water. The suspended particles are visible under a microscope and will settle over time if left undisturbed.

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Which of the following is an advantage of visible light space-telescopes have over ground-based telescopes?
Group of answer choices

They are cheaper

They have a larger telescope diameter

They are easier to repair

They don't have to deal with the Earth's atmosphere

Answers

Answer:

They don't have to deal with the Earth's atmosphere

Explanation:

Space telescopes have the advantage of being above the blurring effects of the Earth's atmosphere

Calculate the mass in grams of the solute ( sulfuric acid ) in 2. 00 ml of 18. 5 m h2so4, concentrated sulfuric acid.

Answers

The mass of sulfuric acid in 2.00 mL of 18.5 M [tex]H_{2} SO_{4}[/tex] is 37.0 mg. Sulfuric acid has a molar mass of 98 g/mol.

To calculate the mass of sulfuric acid in 2.00 mL of 18.5 M [tex]H_{2} SO_{4}[/tex], we need to first convert the volume from milliliters to liters and then multiply that by the concentration in moles/liter. Then, we can multiply the number of moles by the molar mass to get the mass in grams. The mass of 2.00 mL of 18.5 M [tex]H_{2} SO_{4}[/tex] is:

(2 x [tex]10^{-6}[/tex] L) x (18.5 mol/L) x (98 g/mol) = 37.0 mg.

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a computer that adds a few OH ions to water

Answers

A compound that adds a few OH ions to water is referred to as a base.

What is a Base?

This is referred to as a substance that can neutralize the acid by reacting with hydrogen ions. Most of them are minerals that react with acids to form water and salts and some examples include the oxides, hydroxides of metals etc.

They are also known as any compound that yields hydroxide ions (OH-) when dissolved in water thereby resulting in its addition and is the reason it was chosen as the correct choice.

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How many grams of sucrose do you need to make 400mL of a 0.2M solution? The molar mass of sucrose is 342.297 g/mol.

Answers

Molarity is also defined as the moles of a solute per liters of a solution. 1.36 grams of sucrose do you need to make 400mL of a 0.2M solution.

What do you mean by molarity ?

The term molarity (M) is defined as the amount of a substance in a certain volume of solution. Molarity is also defined as the moles of a solute per liters of a solution.

Given:

Molar mass of sucrose, M= 342.297 g/mol.

Volume of the solution,V= 400mL=0.4L

Molarity, S= 0.01M

Mass of the sucrose,W=?

W =S M V

= 0.01 × 342.297 ×0.4

= 1.36 grams

Thus, 1.36 grams of sucrose do you need to make 400mL of a 0.2M solution.

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which of the states of matter have the most energy?

Answers

Plasma is the states of matter which have the most energy. Generally, there are four states of matter.

Plasma is one of four states of matter portrayed by the presence of a critical piece of charged particles in any mix of particles or electrons.[1] It is the most plentiful type of conventional matter known to man, being for the most part connected with stars, including the Sun Reaching out to the thin intracluster medium and potentially to intergalactic locales, plasma can be falsely created by warming an unbiased gas or exposing it to a solid electromagnetic field.

The presence of charged particles makes plasma electrically conductive, with the elements of individual particles and plainly visible plasma movement administered by aggregate electromagnetic fields and exceptionally delicate to remotely applied fields.The reaction of plasma to electromagnetic fields is utilized in numerous cutting edge gadgets and advances, for example, plasma TVs or plasma etchin

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hellpppp pleaseeee !!! under immense pressure and immense heat the protons at the center will _______ together.

Answers

The process of nuclear fusion will occur.

What will protons at the center do under immense pressure and immense heat ?

Under immense pressure and heat, protons at the center of an object can undergo a process called nuclear fusion, where two or more atomic nuclei combine to form a heavier nucleus, releasing a large amount of energy in the process. This is the process that powers stars, including our sun.

In the core of a star, for example, the immense pressure and heat cause hydrogen nuclei (protons) to collide and fuse together to form helium nuclei. This process releases a tremendous amount of energy in the form of light and heat, which ultimately keeps the star shining and stable.

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does freezing involve the creation of a crystal structure

Answers

The majority of liquids freeze through crystallisation, which is the development of crystalline solid from the homogeneous liquid.

Does freezing create a crystal structure?

Because the oxygen atom draws a greater proportion of electrons, the water molecule is slightly positive on one side and slightly negative on the other. The hexagonal crystal lattice is formed when bipolar molecules in water freeze and are drawn near one another.

When a liquid's molecules slow down enough to attract one another and organise themselves into stable places as a solid, freezing happens. Salt water is cooled to create pure ice crystals during the freezing process, also known as crystallisation.

When atoms, molecules, or ions are grouped in a highly ordered microscopic structure, the result is a substance known as a crystal. Chemical bonds such as metallic bonds, ionic bonds, covalent bonds, van der Waals bonds, and others serve as the interatomic forces that hold these components together.

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What resources are shared between threads? tell about what the climb miley cyrus What is the acceptance rate at SUNY Polytechnic? Who Reads an American Book? IV. Long Answer and Analysis (20 points) Do a simple Price Elasticity of Demand Calculation: ; A. If an original price was $5.00 and the amount bought (purchased) was an amount of 50 units (say of good like McDonalds Big Macs). What is the Revenue the producer receives at this point: $________ B. Now the price is lowered to $4.00 and now 200 Big Macs are purchased. What is the new revenue at this point: has it gone up or down?C. using the formula for Price elasticity of Demand, calculate the actual fraction value of the change In price what does swot stand for Tricia needs to bring cookies and fruit to her class of 16 students. There will be a total of 48 items, including 1 piece of fruit for each student. CAN SOMEONE HELP WITH THIS QUESTION?Describe what happens to Copper Sulfate Pentahydrate when you heat it? 1. Cuando Ral y Esperanza llegaron a una fiesta quedaban 3/10 del pastel, as que se dividieron esa porcin en partes iguales. Qu parte del pastel completo le toc a cada uno? what is enneagram test eclecticenergies A car drove at 65 miles perhour for 7 hours. Howmany miles are left if theentire trip is 540 miles? what is a pathogen and what are the four types of pathogens? Evaluate the following expression by drawing the unit circle and the appropriate right triangle. The angle is in radians.cos(5/3) Mark was told his dinner would be ready at 6:00 he left his house at 12:00 and traveled in his car at an average speed of 45mph to his moms house 300 miles away did mark make it to dinner on time In a study of television viewing habits, it is desired to estimate the average number of hours teenagers spend watching per week. If it is reasonable to assume = 3.2 hours, how large a sample is needed so that it will be possible to assert with 95 percent confidence that the sam mean is off by at most 20 minutes? When was notes of a native son published In XYZ, X=81 and Y=22. XWZ=90 and XY=180. Find the length of XW to the nearest integer. Please help me answer this math problem! Let us now consider the Schrdinger Equation for an electron confined to a two dimensional box, 0and 0. That is to say, within this rectangle the electron wavefunction behaves as a free particle ( V(x,y)=0), but the walls are impenetrable so the wavefunction (x,y,t)=0at the walls.3.11.1.svgFigure 1: A particle in a ab2-dimensional box with infinite height can only be found within the box (highlighted). (CC BY-NC; mit Kaya)Extending the (time-independent) Schrdinger equation for a one-dimensional system22md2(x)dx2+V(x)(x)=E(x)(1)to a two-dimensional system is not difficult22m(2(x,y)x2+2(x,y)y2)+V(x,y)(x,y)=E(x,y).(2)Equation 2can be simplified for the particle in a 2D box since we know that V(x,y)=0within the box and V(x,y)=[infinity]outside the box, ii.e.V(x,y)=0[infinity][infinity]0xaand0ybxaybSo Equation 2becomes22m(2(x,y)x2+2(x,y)y2)=E(x,y).(3)Since the Hamiltonian (i.e. left side of Equation 3) is the sum of two terms with independent (separate) variables, we try a product wavefunction like in the Separation of Variables approach used to separate time-dependence from the spatial dependence previously. Within this approach we express the 2-D wavefunction as a product of two independent 1-D components(x,y)=X(x)Y(y).(4)This ansatz separates Equation 3into two independent one-dimensional Schrdinger equations22m(d2X(x)dx2)=xX(x).(5)22m(d2Y(y)dy2)=yY(y).(6)where the total energy of the particle is the sum of the energies from each one-dimensional Schrdinger equationE=x+y(7)The differential equations in Equations 5and 6are familiar as they were found for the particle in a 1-D box previously. They have the general solutionX(x)=Axsin(kxx)+Bxcos(kxx)(8)Y(y)=Aysin(kyy)+Bycos(kyy)(9) An object is spun around in a circle of radius 1. 0 m with a period of 4. 0 s. What is the magnitude of the velocity?.