atoms initially absent from a crystalline solid but deposited
uniformly at time t = 0 on the surface x = 0 of the semi-infinite
solid. The number of radioactive atoms deposited at t = 0 is C per
unit surface area. Show that the concentration of radioactive atoms
n (number per unit volume) in the solid must satisfy the diffusion
equation ∂n/∂t = D ∂^2n/∂x^2 . (7.79) Equation (7–79) can be
obtained by first deriving the equation of conserva- tion of tracer
atoms ∂n/∂t = −∂J/∂x, (7.80) where we assume that tracer atoms
diffuse in the x direction only. The actual decay of the tracer
atoms has been ignored in formulating the mass balance. Solve
Equation (7–79) subject to the initial and boundary conditions. n
(x,t = 0) = 0 (7.81) 0 ∫ ∞ n (x,t) dx = C. (7.82)
Note that this derivation will mirror the derivation of the heat
equation
almost exactly, and the solution will mirror the thermal problem in
section 4-21 almost
exactly. Points are given for clearly drawing out the problem,
defining terms, and
explaining the derivation & solution. (Turcotte Schubert Second
Edition)
- Consider The One Dimensional Diffusion Of Radioactive Tracer Atoms Initially Absent From A Crystalline Solid But Deposit 1 (495.7 KiB) Viewed 40 times