= Solution
For isotropic planar motion, the <planar effusion flux> gives an escape rate through a gap of width $w$ is $\Gamma=w(N/\mathcal A)\langle v\rangle/\pi$, where $\mathcal A$ is tray <area>. At fixed equilibrium <kinetic energy>, or fixed shape of the scaled <speed distribution>, $v\propto m^{-1/2}$. Hence \b[halving the <mass> increases the rate by $\sqrt2$]. This planar <effusion> result assumes the same spatial <density> and an unrestricted small opening. Strictly, average <energy> alone fixes $\langle v^2\rangle$, not $\langle v\rangle$; an arbitrary change of distribution shape would need more information.
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