A solid slab of thickness H₁ is initially at a uniform temperature T₀. At time t = 0, the temperature of the top surface at y = H₁ is increased to T₁, while the bottom surface at y = 0 is maintained at T₀ for t ≥ 0. Assume heat transfer occurs only in the y-direction, and all thermal properties of the slab are constant. The time required for the temperature at y = H₁/2 to reach 99% of its final steady value is τ₁. If the thickness of the slab is doubled to H₂ = 2H₁, and the time required for the temperature at y = H₂/2 to reach 99% of its final steady value is τ₂, then τ₂ / τ₁ is ______