One star exploding won’t do very much! Our galaxy has a few hundred billion stars, plus extra mass in the form of dark matter. If one of those stars explodes, that’s one trillionth of the mass of the whole galaxy exploding. It’s not a big enough event to have a noticeable affect on the galaxy as a whole - one star can only put out so much energy to try and rattle the galaxy.
The explosion can certainly change the visual appearance of the galaxy, if the star is big enough. A supernova can often outshine the entire galaxy the star is living inside - this means as you look at the galaxy, a bright star will suddenly appear, and then gradually fade from view. A supernova in our galaxy was recorded in China in 1006; it was apparently bright enough in the night sky that people were easily able to see at night, and was even visible during the day. However, for a supernova to occur, you need the star to be at least 8 times the size of our sun.
Our sun will not go supernova - it will have a somewhat gentler, although still quite dramatic end of life. It’s predicted to become a planetary nebula, with a white dwarf star as all that remains of our Sun. The process of becoming a planetary nebula doesn’t produce intense shock waves the same way that a supernova does, so while it creates wonderful pictures, it won’t even affect the local area around the sun very much, let alone the whole galaxy.
What an exploding star does do for any galaxy is provide all the heavier elements to the gas hanging about within a galaxy. Then, the next time a star forms in that area, it will have those elements to work with. Any element heavier than iron - for instance, all the gold and silver we have on earth - was formed in an older star’s supernova.
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