In the novel Dandelion Slap, the second book of the Gaia's Wasp trilogy, a government official claimed our atmosphere shields us like three feet of solid lead. Was he right?
Let's consider one square centimeter of dirt, about half the size of a dime. That dirt supports a skinny column of air that reaches all the way up to space, roughly a hundred miles. How tall would the column be, if the air were replaced by the same mass of Lead?
Sea-level air pressure, which is just the weight of our atmosphere, is 14 lbs per square inch. This is 2.2lbs/cm2 = 1kg/cm2.
In other words, each square centimeter of Earth support a skinny column of air that weighs one kilogram. Suppose that column of air was replaced by a column of Lead with the same weight. How tall would it be?
Lead has a density of 11g/cm3, so a one-kilogram lead column must contain 1,000 g / (11 g/cm3) = 91 cm3. If its cross-sectional area is 1 cm2, then its height must be 91 cm, or 36 inches.
In other words, we live under the gaseous equivalent of a three-foot-thick lead slab.
Three feet of Lead is pretty impressive. No wonder it blocks cosmic rays. Would it protect us from the boxcar full of gold?