A 11 gram sample of substance that's used to treat thyroid disorders s has a k-value of 0.1247

You don't have a question but I'll answer what I can.

half-life = natural log (.5) / k

half-life = -.693147 /.1247

half-life = 5.561106656

It seems you did not express the k-value properly.

1) A k-value should have a negative value.

2) A k-value should also have units.

For example, the k-value of tungsten 181 is

-0.005723757 / days