Zirconium is a shiny whitegray metal with a density of 652gm

Zirconium is a shiny white-gray metal with a density of 6.52g/mL and an atomic mass of 91.224g/mol. Each atom (mass = 1.5148e-25kg) will have KE equal to 3/2 k_B T and PE (in the bonds) equal to 3/2k_B T. a) If we converted all the thermal energy at T = 300K into pure translational kinetic energy, how fast will a block of Zirconium travel? b) An alpha particle with 6MeV or 9.613e-13 J of kinetic energy strikes a pellet of Zirconium with mass = 2.00g. Suppose all the kinetic energy is deposited as heat. How many particles will be needed to increase the temperature of the sheet by 10 K? (Pu-238 is a great source of 6MeV alpha particles for use in an RTG.) c) The linear thermal expansion coefficient for Zirconium is 5.5ppm/K. What is the % increase in the volume of the pellet in b) if the temperature increased by 20 K?

Solution

Thermal energy = 3nkT = 3n*1.38*10^-23 T [ where n is the number of atoms]
density, rho = 6.52*10^3 kg/m^3
M = 91.224 g / mol
let mass of the block be m
m = nM
KE = 0.5mv^2 = 3n*1.38*10^-23 *300 = 0.5*nM*v^2
v = 5.2182*10^-10 m/s

b) Ke = 9.613*10^-13 J
KE = 3nkT
n = 9.613*10^-13/3*1.38*10^-23*10
n = 0.2321*10^10 particles
c) For 20 K, change = 5.5*20 = 110 ppm = 110*100/10^6 = 0.011 pc