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# Atoms & Molecules

### States of atoms

A water molecule can vibrate in various ways, but the easiest type of vibration to excite is the "flexing" mode in which the hydrogen atoms move toward and away from each other by the HO bonds do not stretch. The oscillations of this mode are approximately harmonic, with a frequency of 4.8 x 10^13 Hz. As for any quantum harm

### Find the coordinate of the center mass of the sulfur dioxide

The drawing shows a sulfur dioxide molecule. It consists of two oxygen atoms and a oxygen atom. Find the coordinate of the center mass of the sulfur dioxide molecule. See attached file for full problem description.

### kinetic energy of electron and ground state of hydrogen atom

An electron has a de Broglie wavelenght equal to the diameter of the Hydrogen atom. What is the kinetic energy of the electron? How does this energy compare to the ground state of the hydrogen atom?

### Distance Between Particles and Energy in Positronium

Positronium is an atom composed of an electron and a positron (mp = me, Q = +e). Calculate the distance between the particles and the energy of the lowest energy state of positronium. Hint: the reduced mass µ of the two particles equals me/(1 + me/m). -----------------a0 ------------------E0

### Elastic Collision of two atoms in two dimensions

Please help me solve the following: An atom of mass m moving in the x direction with speed v collides elastically with an atom of mass 3m at rest. After the collision, the first atom moves in the y direction. Find the direction of motion of the second atom and the speeds of both atoms (in terms of v) after the collision. ---

### Root-mean-square speed

What is the root-mean-square speed of chlorine gas molecules at a temperature of 47 degrees C? (Molecular mass of Cl2 = 71)

### Nuclear Energy and Elementary Particles

1.) It has been estimated that the Earth contains 1.0 x 10^9 tons of natural uranium that can be mined economically. If all the world's energy needs (7.0 x 10^12 J/s) were supplied by 235(U) fission, how long would this supply last? Assume that the average energy released in a fission event is 208 MeV. (Hint: 235/92(U) has a per

### Free Electron Theory

(a) (i) What are the main assumptions of the free electron model? (ii) Give an example where the free electron model is in good agreement with experiment. (iii) Give an example where the free electron model fails. (b) (i) How does the nearly free electron model improve on the free electron model? (ii) Describe one of the s

### Pressure of a Nitrogen Particle Striking a Wall.

In a period of 1.00 s, 8.00 x 10^23 nitrogen molecules strike a wall with an area of 7.40 cm^2. If the molecules move with a speed of 300 m/s and strike the wall head-on in elastic collisions, what is the pressure exerted on the wall? (The mass of one N2 molecule is 4.68 x 10^-26 kg.) Answer in KiloPascals

### Order of Magnitude Calculations

Legend has it that, many centuries ago, Archimedes jumped out of his bathtub and ran across town naked screaming "Eureka!" after he solved an especially difficult problem. Though you may not have thought of things this way before, when you drink a glass of water, the water that you are drinking contains some water molecules that

### Intro to Quantum Mechanics

Could some please give detailed soltions to the following past paper Question 2. Please highlight where standard formulas (showing the formulas in bold) are used and make all methods clear explaining what has been done and why.

### Physics Problems

How does the number of atoms in a 26.5 gram gold ring compare to the number in a silver ring of the same mass? Amoung the higest and lowest temperatures recorded are 136degrees F in the Libyan desert and -129Degrees F in the Antarctica. What are these in Celsius? To make a secrue fit, rivets that are larger than the rivit

### Solving: Kinetic Theory of Gases

Hi, I need some assistance with the following problems: 1. If the translational rms speed of the water vapor molecules (H2O) in air is 664 m/s, what is the translational rms speed of the carbon dioxide molecules (CO2) in the same air? Both gases are at the same temperature. 2. Near the surface of Venus, the rms speed of c

### Molecules

What kinds of evidence supports the belief that molecules of various kinds, including some complex ones, exist in space? Please include references to support answer.

### Calculating force, power, equilibrium, and energy

1. A Ping-Pong ball has a diameter of 3.8 cm and average density of 0.084 g/cm3. What force is required to hold it completely submerged under water? 2. A tank with a cover, containing a liquid of density p, has a hole in its side at the distance y1 from the bottom. The diameter of the hole is small relatively to the diamete

### Harmonic function and vibrational energy states

Why can a harmonic function be used to compute vibrational energy states for a DIATOMIC molecule, and under what conditions are the computed values inaccurate?

### Vibrating Hydrogen Molecule

When displaced from equilibrium by a small amount, the two hydrogen atoms in an H_2 molecule are acted on by a restoring force F_x = k_1*x with k_1 = 650 N/m. Calculate the oscillation frequency f of the H_2 molecule. Use m_eff = m/2 as the "effective mass" of the system, where m in the mass of a hydrogen atom. Take the mass of

### Interstellar space: pressure, rms speed of the atoms

Interstellar space, far from any stars, is filled with a very low density of hydrogen atoms (H, not H_2). The number density is about 1 atom/cm^3 and the temperature is about 3K. A & B) Estimate the pressure in interstellar space. Give your answer in Pa and in atm. C) What is the rms speed of the atoms? D) What is the e

### The Speed of Nitrogen Molecules

The Speed of Nitrogen Molecules The kinetic theory of gases states that the kinetic energy of a gas is directly proportional to the temperature of the gas. A relationship between the microscopic properties of the gas molecules and the macroscopic properties of the gas can be derived using the following assumptions: • The ga

### Water condensation

Please do not place your response in a .pdf or .cdx format, but Word documents are okay. Thanks! Here's the actual problem: 3x10^4 cm^3 of 400 degrees Celsius steam at a pressure of 20.0 atm is cooled until is condenses. What is the volume of the liquid water? Give your answer in cm^3.

### Multiple Choice Questions

1. Nitrogen may be combined with oxygen in proportion by mass of 1.75 g nitrogen to 1.00 g oxygen to form the gas nitrous oxide, N2O. The same elements may be combined in the ratio of 0.438g nitrogen to 1.00g oxygen. What is the atomic composition of the second compound? a. NO(2) b. NO c. N(2)O d. NO(3) 2. I

### Molecular Mass, the Mole, and Avagadro's Number

Question: The artificial sweetener NutraSweet is a chemical called aspartame (C14 H18 N2 O5). A) What is its molecular mass (in atomic units)? B)What is the mass (in kg) of an aspartame molecule?

1) Polymers, like rubber, are made of very long molecules, usually tangled up. Another very crude model of a rubber band is that each link is either crumbled up or stretched. If it is crumbled up, its length is negligible and it is in the lowest energy state, call it E = 0. If it is stretched, then its length is L and it is in

### Frequency and hydrogen atom transition

Find the frequency of the light that corresponds to a transition in the hydrogen atom from the n=7 state to the n=2 state.

### Max wavelength if a photon and ionization

Find the maximum wavelength of the photon that a hydrogen atom in its ground state must absorb in order for the ionization to occur.

### Body water question

Assume that the human body is 75% water. How many moles of water are in your body? How many molecules? If I am 75% water, then why am I always getting thirsty? My body weight is 165lbs.

### Physics: Calculate molecular mass and moles of a chlorophyll-a molecule.

The chlorophyll-a molecule, C55H72MgN4O5, is important in photosynthesis. (a) Determine its molecular mass (in atomic mass units). (b) What is the mass (in grams) of 3.00 moles of chlorophyll-a molecules?

### Calculating the center of mass of a molecule

The carbon monoxide molecule (CO) consists of a carbon atom and an oxygen atom separated by a distance of 1.13 * 10^-10 m. The mass of mc = 0.750 mo. Determine the location of the center of mass of this molecule relative to the carbon atom.

### Interaction between two atoms

A commonly used potential energy function to describe the interaction between two atoms is the Lennard-Jones potential U=e((Ro/R)^12-2(Ro/R)^6) a) Show that the radius at the potential minimum is Ro, and that the depth of the potential well is e. b) Find the frequency of small oscillations about equilibrium for 2 identi

### Estimate the total number of electrons in any molecule

If you remove all the electrons from a rain drop (diameter = 1 mm), what would be the gain in the electrostatic potential of the entire earth? Consider the radius of the earth to be R=6378.14 km. The answer clearly in by the simplest way illustrates the solution.