Balloons are still used to deploy sensors that monitor meteorological phenomena and the chemistry of the atmosphere. It is possible to investigate some of the technicalities of ballooning by using the perfect gas law. Suppose your balloon has a radius of 3.0 m and that it is spherical.

(a) What amount of H₂ (in moles) is needed to inflate it to 1.0 atm in an ambient temperature of 25°C at sea level?

(b) What mass can the balloon lift at sea level, where the density of air is 1.22 kg m⁻³ ?

(c) What would be the payload if He were used instead of H₂?