 Solution

An inertially confined sphere disassembles on approximately $\tau \sim r/c_s$, while $n_i=\rho /{\bar{m}}_i$. Substitute these in the given number-density confinement product to getFor an equal D-T mix, ${\bar{m}}_i\simeq 2.5m_u$. Taking $c_s\sim \sqrt{2k_{B}T/{\bar{m}}_i}$ at 10 keV gives $A\simeq 0.365$ kg m${}^{-2}=0.0365$ g cm${}^{-2}$. An adiabatic sound-speed convention changes this by an order-one factor. This estimate implements the supplied Lawson product and is not the separate, more stringent alpha-stopping areal-density criterion.