A Monte Carlo program draws helium atom speeds from a Maxwell-Boltzmann distribution…

PHYSICS · Subjective · Fermi University Physics · Computational Physics · Monte Carlo and lattice simulation of physical systems · Monte Carlo and lattice simulation of physical systems

Computational Physics, Ch Drawing numbers: random walks and Monte Carlo

Problem

A Monte Carlo program draws

N = 2000

helium atom speeds from a Maxwell-Boltzmann distribution (seed

5

) to estimate the mean speed at a stated temperature, obtaining

\bar v = 450 \pm 6\,\mathrm{m\,s^{-1}}

. (a) Using the

1/\sqrt{N}

law for the standard error of a Monte Carlo mean, find the number of draws

N'

that would be needed, by the same method, to bring the standard error down to

1.5\,\mathrm{m\,s^{-1}}

. (b) Predict the standard error expected if instead

N'' = 18\,000

draws are used (seed

6

). (c) That run actually gives

\bar v = 447 \pm 2.1\,\mathrm{m\,s^{-1}}

. Compute the percentage difference between this measured standard error and the prediction of part (b), and say whether it is a meaningful discrepancy given that a standard-error estimate from

N

draws itself carries a relative uncertainty of about

1/\sqrt{2N}

Browse the problem library