A semiconductor crystal at T₁ = 263 K, X₁ = 1 mm thick, has one surface illuminated with light, so that free carriers (electrons and holes) are generated at the surface. The carriers diffuse away into the sample. (Note that the electrons appear to head to the right only because there is nothing on the left.) An observable number of carriers makes it across the crystal, 1 mm (in the x-direction) after t₁ = 125.4 μs.

When we illuminate an identical crystal, but at T₂ = 300 K, and of an unknown thickness X₂, we measure that it takes an observable number of carriers t₂ = 627.1 μs to cross it. You may assume for this problem that all the carriers have the same mass, that of a free electron (m_e = 9.11 X 10^-31 kg), and that the mean scattering length remains constant over the range of temperatures in the problem.

How thick is the second crystal ?

X₂ = mm