How long would a blasting ray of Kryptonite approximately take to kill Supergirl?

And has Supergirl in the comics or the TV series with Melissa Benoist ever openly conceded defeat and then pleaded with her enemies to let her go.

https://www.youtube.com/watch?t=200&v=C8SN4ND6olY&feature=youtu.be

The following video is from a Russian fan-film production of Supergirl.