Answer Happy

Problem 6.17. The most common measure of the fluctuations of a set of numbers away from the average is the standard deviation, defined as follows. (a) For each atom in the five-atom toy model of Figure 6.5, compute the devi- ation of the energy from the average energy, that is, E₁-E, for i = 1 to 5. Call these deviations ΔΕ.. (b) Compute the average of the squares of the five deviations, that is, (AE₁) ². Then compute the square root of this quantity, which is the root-mean- square (rms) deviation, or standard deviation. Call this number og. Does E give a reasonable measure of how far the individual values tend to stray from the average? (c) Prove in general that o=E² - (E)², that is, the standard deviation squared is the average of the squares minus the square of the average. This formula usually gives the easier way of computing a standard deviation. (d) Check the preceding formula for the five-atom toy model of Figure 6.5. -2.1 11
Figure 6.5. Five hypothetical atoms distributed among three different states. Energy 7 eV 4 eV
where E is the energy of the atom. Plugging this expression back into equation 6.2, we obtain P(82) P($1) = e-[E(82)-E(31)]/KT e-E(2)/kT e-E(81)/kT (6.5) The rotic =