(Solved): d. HII regions can exist only if there is a nearby star hot enough to ionize hydrogen. Hydrogen is ...

d. HII regions can exist only if there is a nearby star hot enough to ionize hydrogen. Hydrogen is ionized only by radiation with wavelengths shorter than $91.2\mathrm{nm}$. What is the temperature of a star that emits its maximum energy at $91.2\mathrm{nm}$ ? Based on this result, what are the spectral types of those stars likely to provide enough energy to produce $\mathrm{H}I\mathrm{I}$ regions? 3. Calculate the radii of black holes with masses equal to the following. 5 bonus points will be rewarded if you do this in Python and provide a screenshot of your code. a. Earth b. The Sun c. $8\mathrm{M}$ d. Our supermassive black hole, Sagittarius ${\mathrm{A}}^{\ast }\left(4\times 10^6\mathrm{M}\right)$ 4. The star Arcturus is also located roughly $8\mathrm{kpc}$ from the center of the galaxy and is moving with a circular velocity of $122\mathrm{m}/\mathrm{s}$. How long does it take Arcturus to go through one full rotation around the galaxy?