Final answer:
The volume of a cylindrical galaxy with a diameter of 100,000 light-years is approximately 2.0 × 1066 cm3. The mass of hydrogen gas within this volume can be calculated, leading to an estimation of the number of solar-mass stars that could be formed from this gas.
Step-by-step explanation:
If the galaxy is assumed to be a cylinder with a diameter of 100,000 light-years, then the radius would be 50,000 light-years. Given that 1 light-year is equivalent to 9.5 × 1017 cm, we can calculate the volume of the galaxy using the formula for the volume of a cylinder, V = πR2h. Using this formula and the given conversion for a light-year in centimeters, we can find the volume of the galaxy as V = π(50,000 × 9.5 × 1017 cm)2 × (300 × 9.5 × 1017 cm), which equals approximately 2.0 × 1066 cm3.
Furthermore, if we assume that the average density of hydrogen gas in our Galaxy is one atom per cm3 and each hydrogen atom has a mass of 1.7 × 10-27 kg, we can calculate the mass of the gas in the galaxy by multiplying the volume by the mass of a single atom. Following these calculations, we can also determine the number of solar-mass stars that could potentially be produced from this mass of gas if all of it were turned into stars. A solar-mass star has a mass of 2.0 × 1030 kg, so by dividing the total mass of the hydrogen gas by this mass, we can estimate the number of such stars.