Consider a system of n interacting molecules, whose vibrational degrees of freedom are treated with qm, and whose translational and rotational degrees of freedom are treated classically with the hamiltonian: hclass = ktrans + krot + u where k is kinetic energy, and u is a potential energy. derive the expression: prob(ktrans) = e −ktrans kt dptrans ∫ e −ktrans kt dptrans by starting from: q = qqm n! h sn ∫ e hclass kt dpclass dqclass given that: ktrans = ∑ 1 2m n j=1 (px, j 2 + py, j 2 + pz, j 2 ) derive the normalized maxwell-boltzmann distribution: f(px , py, pz)dpxdpydpz = (2πmkt) −3/2 e −(px 2+py 2+pz 2) 2mkt dpxdpydpz

the order for strong to weak forces such as

strong nuclear force → electromegnetic force → weak nuclear force → gravitational force

the fundamental forces are those forces that act between to objects or element to make interactions. there are four types of fundamental forces such as strong and weak nuclear forces (due to protons and electrons), electromagnetic force (due to the motion of electrons) and gravitational force (due to orbital movement of the planet). if these forces are arranged on the basis of their maximum strength then the order is

strong nuclear force → electromegnetic force → weak nuclear force → gravitational force

maria has a savings account that is earning simple interest. if she started with $200 in the account and has earned a total of $8 in interest in two years, what is the rate of the account? use the formula  .