(a) How are the boundaries between the regions of the atmosphere determined? (b) Explain why the stratosphere, which is about \(35 \mathrm{~km}\) thick, has a smaller total mass than the troposphere, which is about \(12 \mathrm{~km}\) thick.

Determining the boundaries between the regions of the atmosphere involves examining the changes in temperature with respect to altitude. Different atmospheric layers exhibit distinct vertical temperature profiles. The boundaries between these layers are marked by regions where the temperature gradient either changes significantly or remains constant.

Before we answer why the stratosphere has a smaller mass than the troposphere, even though it is thicker, we need to understand how atmospheric pressure works. Atmospheric pressure is the force exerted on a surface due to the weight of the air above it. As altitude increases, atmospheric pressure decreases because there is less air mass above that point.

Atmospheric density and pressure both decrease exponentially with increasing altitude. This is because, as we go higher up in the atmosphere, the gravitational force acting on the air molecules decreases, and they become more widely spaced apart. This decrease in density causes a corresponding decrease in atmospheric pressure.

Now, we will compare the masses of the troposphere and stratosphere. As mentioned earlier, atmospheric pressure decreases with increasing altitude. Since the base of the troposphere is at the Earth's surface, where the atmospheric pressure is at its highest, the troposphere contains a significant proportion of the total atmospheric mass. The troposphere is also more densely packed with air molecules compared to the stratosphere. The stratosphere, on the other hand, starts at a higher altitude where the atmospheric pressure and density are both lower than in the troposphere. Even though it extends up to 35 km, the total mass of the stratosphere is less than that of the troposphere because the air density and pressure are lower in this layer, making the air molecules more scattered. In conclusion, even though the stratosphere is physically thicker than the troposphere, its total mass is smaller due to the lower air density and pressure in this atmospheric layer.