$18\mathrm{.}64.$ A person at rest inhales $0\mathrm{.}50L$ of air with each breath at a

pressure of $1\mathrm{.}00$atm and a temperature of $20\mathrm{.}0C.$ The inhaled air

is $21\mathrm{.}0\%$ oxygen. $($a$)$ How many oxygen molecules does this per$-$

son inhale with each breath? $($b$)$ Suppose this person is now resting

at an elevation of $2,000m$ but the temperature is still $20\mathrm{.}0C.$

Assuming that the oxygen percentage and volume per inhalation

are the same as stated above, how many oxygen molecules does

this person now inhale with each breath? $($c$)$ Given that the body

still requires the same number of oxygen molecules per second as

at sea level to maintain its functions, explain why some people

report "shortness of breath" at high elevations.