Boltzmann distribution Definition and 70 Threads

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...

Hi all, can anyone see what is going wrong in the following problem please (this is really important, so if you have any hints that would be fantastic!) The restoring force corresponding to a change in length of the bnd between Hydrogen atoms in H2 is k = 2400 N/m, find the fraction of...

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...

Physical systems are analog computers and sample their states according to Boltzmann distribution, this is what usually taken as granted in solving so many problems in statistical physics. what actually is the physics of Boltzmann distribution...anyone...?