In a certain physical system, there are two energy states available to a particle: the ground state with energy E₁ = 0 eV, and the excited state with energy E₂ = 1.5 eV. The system is in thermal equilibrium at a temperature T = 300 K. Calculate the Gibbs factor (also known as the Boltzmann factor) for the excited state . Give your answer to two decimal places.

In a certain physical system, there are two energy states available to a particle: the ground state with energy E₁ = 0 eV, and the excited state with energy E₂ = 1.5 eV. The system is in thermal equilibrium at a temperature T = 300 K. Calculate the Gibbs factor (also known as the Boltzmann factor) for the excited state . Give your answer to two decimal places.

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter21: Heat And The First Law Of Thermodynamics

Section: Chapter Questions

Problem 78PQ

See similar textbooks

Similar questions

The number N of atoms in a particular state is called the population of that state. This number depends on the energy of that state and the temperature. In thermal equilibrium,the population of atoms in a state of energy En is given by a Boltzmann distribution expression N = Nge-(En-Eg)/kBTwhere Ng is the population of the ground state of energy Eg , kB is Boltzmann’s constant, and T is the absolute temperature. For simplicity, assume each energy level has only one quantum state associated with it. (a) Before the power is switched on, the neon atoms in a laser are in thermal equilibrium at 27.0°C. Find the equilibrium ratio of the populationsof the states E4* and E3 shown for the red transition in the figure. Lasers operate by a clever artificial production of a “population inversion” between the upper and lower atomic energy states involved in the lasing transition. This term means that more atoms are in the upper excitedstate than in the lower one.…
These two questions relate to the Boltzmann Equation. A gas of neutral hydrogen atoms in local thermodynamical equilibrium has 1/3 more atoms in the energy level n = 1 than in the n = 2 state. Calculate the temperature of that gas. For a gas of neutral hydrogen atoms make a graph that shows the ratios N2/N1, N3/N1, N4/N1 as a function of T.
An expensive vacuum system can achieve a pressure as low as 1.00 x 10-8 N/m² at 21.5 °C. How many atoms N are there in a cubic centimeter at this pressure and temperature? The Boltzmann constant k = 1.38 x 10-23 J/K. O 2.46 x 106 atoms O 2.44 x 104 atoms O 2.46 x 105 atoms O 2.46 x 107 atoms O 2.46 x 108 atoms
Assume that the Maxwell-Boltzmann distribution is valid in a gas of atomic hydrogen. What is the relative number of atoms in the ground state and first excited state at 293 K (room temperature), 5000 K (the temperature at the surface of a star), and 106 K (a temperature in the interior of a star)?
An expensive vacuum system can achieve a pressure as low as 1.00 x 10-7 N/m² at 25.5 °C. How many atoms N are there in a cubic centimeter at this pressure and temperature? The Boltzmann constant k = 1.38 x 10-23 J/K. N = atoms
A container holds N molecules of nitrogen gas at T = 280 K. Find the number of molecules with kinetic energies between 0.0300 eV and 0.0312 eV.
How does the Boltzmann distribution and statistics explain the behavior of an ideal gas in terms of the distribution of molecular energies and the probability of various energy states?
In the simple kinetic theory of a gas we discussed in class, the molecules are assumed to be point-like objects (without any volume) so that they rarely collide with one another. In reality, each molecule has a small volume and so there are collisions. Let's assume that a molecule is a hard sphere of radius r. Then the molecules will occasionally collide with each other. The average distance traveled between two successive collisions (called mean free path) is λ = V/(4π √2 r2N) where V is the volume of the gas containing N molecules. Calculate the mean free path of a H2 molecule in a hydrogen gas tank at STP. Assume the molecular radius to be 10-10 a) 2.1*10-7 m b) 4.2*10-7 m c) none of these.
Consider the Universe to be spherical, mostly hydrogen gas molecules undergoing adiabatic expansion over its lifetime. a. Using the ideal gas law and properties of adiabatic processes show T V γ − 1= C where C is a constant. b. The current Universe extends at least 15 billion light-years in all directions (r = 1.4 x 1026m), and the current temperature of the Universe is 2.7 K. Estimate the temperature of the Universe when it was the size of a nutshell, with a radius of 2 cm. c. If the density of the gas in the Universe, N/V, is one hydrogen atom per cubic meter, calculate the current pressure of the Universe. d. Estimate the pressure of the Universe when it was the size of a nutshell. (You may get a calculator overflow error)
The density of gray and white tin are 5.77×103 kg/m3 and 7.37×103 kg/m3. The latent heat for the transition between gray and white tin is 2.20×103 J/mol. The atomic weight of tin is 118.7. Calculate the slope of the tangent of the coexistence curve of gray and white tin at T=376 K. Select one: a.dP/dT=−14.2 atm/K b.dP/dT=−12.9 atm/K c.dP/dT=−14.6 Pa/K d.dP/dT=−12.3 Pa/K
Q. 4. A cylinder with a movable piston contains 3 moles of hydrogen at standard temperature and pressure. The walls of the cylinder are made of a heat insulator, and the piston is insulated by having a pile of sand on it. By what factor does the pressure of the gas increase, if the gas is compressed to half its original volume ? Given y= 1.4.
Suppose we have a macroscopic amount (~ moles) of argon gas in thermodynamic equilibrium at STP conditions. In this case, the velocities of the gas atoms follow the Maxwell and Boltzmann distribution with very good accuracy. Which of the following statements is/are true? Select one or more: a. When heating a gas, the ratio of the average speed of the molecules to the most probable speed increases. b.Heating the gas would lead to a shift of the most probable speed of the momentum distribution to a lower value, while the relative number of high-speed atoms would increase. c. Replacing argon atoms with helium atoms would lead to a momentum distribution in equilibrium, the most probable momentum of which would shift to a higher value and the relative number of high-speed atoms would increase.