Your crude measurement suggests that the bullet is .45 caliber. 7/16 = .4375 which is about as close as we are going to get without calipers or micrometer. An actual .45 bullet
would be .452, slightly oversize for a tight fit in the barrel In the photo it looks like there is a copper jacket on the bullet, and the little grooves around the bullet is called the
cannelure. Copper jackets were invented in the 1890's, along with the cannelure grooves, and smokeless powder. But the use of all three didn't really become common until after 1900.
.45 caliber pistol cartridges date to 1873 with the Colt army revolver, however those were
all lead bullets. The most common .45 caliber full metal jacket bullet has got to be for the Colt Automatic Pistol, which was on the market in 1911. With the minimal amount of
information provided, and the fact that .45 ACP is probably the most common copper jacketed bullet close to that size, my swag is you have a model 1911 ACP bullet fired sometime
after 1911.