A balloon has a diameter of 50 cm,and the density of the air in the balloon is 10¹⁹ particles/cm³.You wish to expand the balloon so that its density is 1 particle/cm³ (the average density of the interstellar medium).What is the diameter will the balloon have when its density is 1 particle/cm³? A) 1,100 km B) 1.1*10⁸ km C) 220 km D) 2.2*10⁶ km E) 4.3*10⁴ km

Question

Quizplus · Accepted Answer

The volume of the balloon increases proportionally to the cube of the diameter. The initial density is 10^19 particles/cm^3, and the final density is 1 particle/cm^3, so the volume must increase by a factor of 10^19. The diameter must increase by the cube root of 10^19, which is approximately 10^6.33. Multiplying the initial diameter (50 cm) by this factor gives approximately 1,100 km.

A Balloon Has a Diameter of 50 Cm,and the Density