Even a .38 Special will do the job, but...
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That's another example of the dictum: "...any bullet, regardless of size or caliber, injuring these organs will cause instant incapacitation. It is the nature of the structure injured, not the nature of the bullet that causes incapacitation."
[Regarding the last shot the hunter fired.]

.38 Special Effective Against Wyoming Grizzly Bear
During a grizzly bear attack on archery hunters in September of 2011, one hunter used a .38 Special revolver to stop the attack.

That's another example of the dictum: "...any bullet, regardless of size or caliber, injuring these organs will cause instant incapacitation. It is the nature of the structure injured, not the nature of the bullet that causes incapacitation."
[Regarding the last shot the hunter fired.]