The absorptivity of CO$2$ gas in the atmosphere at the Earth$$s surface is $0\mathrm{.}04$ m$-1$ for infrared radiation of wavelength $15\backslash$mu m$.$ Calculate the distance L for when the radiation intensity for wavelength of $15\backslash$mu m $($I$15)$ has decreased to $1/10$ of the initial at L$=0($I$15$o$).$ Repeat the calculation for L when $($I$15)$ is $1/100$ of $($I$15$o$)$Beer$\text{'}$s Law Applied to Atmospheric $C{O}_2(30pts)$

Infrared radiation emitted from the earth's surface is absorbed by $C{O}_2$ molecules in the air above

the earth's surface. This contributes to the greenhouse effect that helps create a habitable

condition for life. The absorptivity of $C{O}_2$ gas in the atmosphere at the Earth's surface is $0\mathrm{.}04m^{-}$

${?}^1$ for infrared radiation of wavelength $15m.$ Calculate the distance $L$ for when the radiation

intensity for wavelength of $15m(I_{15})$ has decreased to $\frac{1}{10}$ of the initial at $L=0(I_{150}).$ Repeat

the calculation for $L$ when $(I_{15})$ is $\frac{1}{100}$ of $(I_{150}).$