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Atoms & Molecules

Derive an Order of Magnitude Estimate for a Harmonic Oscillator

The oscillation frequencies of a diatomic molecule are typically 10^12hz-10^14Hz. Derive in order of magnitude estimate for the harmonic oscillator constant K for such molecules. I need to know how to do this for a test tomorrow. So detailed solutions please.


Coal is combusted in a steam boiler. The specific coal contains 25 MJ/kg If the boiler is 90% efficient, how much coal must be burned per hour to produce a stream thermal gain of 665 MJ/s. Roughly how much CO2 will be produced by this boiler?

center of mass of the sulfur dioxide molecule

The drawing shows a sulfur dioxide molecule. It consists of two oxygen atoms and a sulfur atom. A sulfur atom is twice as massive as an oxygen atom. Using this information and the data provided in the drawing, find the coordinates of the center of mass of the sulfur dioxide molecule. Express your answers in nanometers (1 nm = 10

Writing Matrix Equations and Programs for Spring Mass System

13. Consider the spring mass system (see attached file) (a simple model of a short polymer molecule). The blocks are free to move but only along the x-axis. The springs connecting adjacent blocks have spring constant k1, while the two outer springs have stiffness k2. All the springs have a rest length of one. (a) Write the matri

Calculate the rotational partition function for CO molecule

For a CO molecule, the constant epsilon is approximately 0.00024 eV. Calculate the rotational partition function for a CO molecule at room temperature (300 K), first using the exact formula: (j = 0 to ∞) Zrot = sum of (2j + 1)e-E(j)/kT = sum of (2j + 1)e-j(j + 1)epsilon/kT, and then using the approximate formula: (

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

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

Weight Density and Pressure of Falling Container

PROBLEM: A cylinder container has a couple of holes punched into the bottom of it and the water is spurting out the holes due to the water pressure. You drop the water filled cylinder and as it is free falling the water no longer spurts out the holes. What happens to g, and hence weight, and hence weight density, and hence

Fermi Problems and Equivalents

3 fermi problems: Q1) Estimate the number of atoms in a Trex? Q2) What is 10amu in kg? Q3) Estimate the number of hairs on a dog?

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.

Atomic States for Absorbed Photon Frequency

(See attached file for full problem description) --- Atoms of lithium are able to absorb photons of frequency 2.01 x 1014 Hz. This corresponds to a transition state from the ground state (at -5.37 ev) to an excited state. Zero energy corresponds to the state in which one electron is completely removed from the atom. (Use

Thermal expansion:

A solid steel plate with a hole through its center, drops in temperature, what will the hole's diameter do?

Moles of Gold and Water

When you compare one mole of gold to one mole of water what will they have in common (same mass, volume or number of molecules)?

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

Charge on the Electrons in a Nickel Coin

We want to find how many Coulombs of charge are on the electrons in a nickel coin. Follow this method. a) A nickel coin has a mass of about 5.172 g. Each mole (6.02 * 10^23 atoms) has a mass of about 57.98 g. Find the number of atoms in nickel coin. b) Find the number of electrons in the coin. Each nickel atom has 28 elect

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


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