Boltzmann distribution Definition and 69 Threads

hi everyone, consider two different masses of ideal gases with different molar masses, we're putting them in a uniform gravitational field and wait until they come to their equilibrium states. how would the density distribution change with height in this case? ( i came out with this question...

Homework Statement The relative population of two atomic population states in equilibrium is given by Boltzmann Distribution: n1/n0 (proportional to) e^(-ε/(κT)) , where ε is the energy difference between the two states, T is the temperature and κ is the Boltzmann constant = (1.38 x...

For N(E)=Aexp(-E/kT), I know that N(E) is the no. of particles with a certain energy E, but why does integrating N(E) from 0 to infinity equal to 1? Although I realize that it means that there is 100% probability to find a particle in this range, I want to know why summing up all no. of...

Homework Statement The first excited state of Ca is reached by absorption of 422.7-nm light. • Find the energy difference (kJ/mol) between ground and excited states. • The degeneracies are g*/g0 = 3 for Ca. Find N*/N0 at 2 500 K. • By what percentage will N*/N0 change with a 15-K rise in...

Homework Statement Compute the mean energy and mean square energy of a free particle using the Boltzmann distribution. Homework Equations The Attempt at a Solution I calculated the mean energy to be 3/2 kT by computing the mean square velocity directly from the Boltmann...

I read http://en.wikipedia.org/wiki/Maxwell%E2%80%93Boltzmann_distribution#cite_note-0 In formula 7 we obtain proportionaly to E^1/2 and exp(-E). But I expect proportionaly to E^-1/2 and exp(-E). Where I am wrong?

What conditions are needed?

Homework Statement Use the maxwell Boltzmann distribution to derive an expression for <v^3> Homework Equations <v>=(8RT/piM)^1/2 The Attempt at a Solution I know that you have to integrate from 0 to infinity v^3p(v)dv.. but I don't really know how to integrate this. I just need to...

The question is: Write an expression for the average energy of a set of particles obeying Boltz- mann statistics and each having energy E = bz2, where b is a constant and z is a variable. Hence, show that the average energy per degree of freedom for each particle is 1 2kBT; where kB is...

I'm using McQuarrie's "Statistical Mechanics" for a class, and I'm not quite understanding the the derivation of the Boltzmann Distribution. I'm going to go through it, and then ask a few questions along the way. All right. You start with a canonical ensemble with N, V, and T fixed. Heat can...

Hi, I have some questions about the derivation of the Boltzmann distribution, for instance as in Mandl's "statistical physics". Put a system (1) in a heatbath (2) with temperature T. In thermal equilibrium system 1 will also then have temperature T. The energy of system (1) is not fixed due to...

I have a question about the Lagrange Multiplier method used to derive the Boltzmann distribution. I'm following the first http://en.wikipedia.org/wiki/Maxwell%E2%80%93Boltzmann_statistics" . I can get to this equation fine: And I understand how they get the next line...

Hello everyone Homework Statement The equivalent of the Maxwell-Boltzman distribution for a two-dimensional gas is P(v) = Cv e^-\frac {mv^2}{kt} Determine C so that \int_0^\infty P(v)dv = NHomework Equations Not really sureThe Attempt at a Solution I wasn't really sure how to tackle this...

Homework Statement The energy difference between the first excited state of mercury and the ground state is 4.86 eV. (a) If a sample of mercury vaporized in a flame contains 10^20 atoms in thermal equilibrium at 1600K, calculate the number of atoms in the n=1 (ground) and n=2 (first-excited)...

The question states: A system has energy levels uniformly spaced at 3.2x10^-10 J apart. Thepopulations of the energy levels are given by the Boltzmann distribution. What fraction of particles is in the ground state at T=300K. I know that the Boltzmann distribution is: _{}p*j=probability...

Hi folks! i'm a biologist trying to understand some basics of statistical mechanics. :wink: unfortunately, i cannot get over the following problem(s). A) in the Boltzmann distribution the fraction of particles with energy Ei is given by: \frac{Ni}{N} = \frac{exp(-\beta Ei)}{\sum...

I apologize if this is the wrong thread but since this relates to thermo I figured this would be a good place to post this question. This is a problem that was assigned to us for physical chemistry but I can't find a good justification for one of the problems. 1. A system containing 38...

We know the Maxwell-Boltzmann distribution for the energy and the speed of a molecule of an ideal gas. Using derivatives it is easy to see that the most probable speed for a gas molecule is given by sqrt(2kT/m), which corresponds to kinetic energy kT. Calculating the most probable energy, we get...

I need to answer the following question: A simple energy level system has two energy levels. These are the energy levels matching the spin of a proton in a magnetic field. This is important for NMR. In that case the energy difference depends on the used magnetic field, but for a typical NMR...