= Solution
Use a steady planar sonic ablation model with absorbed intensity $I_a$, critical <Density>[mass density] $\rho_c=(A_i/Z)m_u n_c$, and $n_c=\epsilon_0m_e(2\pi c/\lambda)^2/e^2$. In the usual isothermal-electron sonic balance, $I_a\simeq4\rho_c c_s^3$ and the ablation <pressure> is $P_A\simeq2\rho_c c_s^2$. Eliminating $c_s$ gives
$$
\boxed{P_A\simeq C(I_a/\lambda)^{2/3},\quad C=\left[\frac{A_i}{Z}\frac{m_u\epsilon_0m_e(2\pi c)^2}{2e^2}\right]^{1/3}.}
$$
For $A_i/Z\simeq2$ and complete absorption, the supplied laser parameters give about $1.15\times10^{13}$ Pa, or $115$ Mbar. Mach one alone fixes neither the material <mass> per <electron> nor the <enthalpy>/<absorption coefficient>. Different sonic-flow closures change the order-one constant; incomplete absorption multiplies the estimate by its fraction to power $2/3$. The robust result is the two-thirds scaling, rather than a material-independent numerical <pressure>.
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