If galium-68 has a half life of 68.3 minutes, how much of a 10.0 mg sample is left after one half life. Two half lives? Three half lives?

The amount of the 10.0mg sample of Galium-68 remaining after;

Irrespective of the half life of an element such as Galium-68; the half-life is the duration of time it takes for the element to remain half it's original mass.

In essence; Since the starting sample of galium-68 has a mass of 10.0mg.

After one half life;

The amount of Galium-68 remaining is; (10/2) mg

After two half lifes;

The amount of Galium-68 remaining is; (5/2) mg

After three half lifes;

The amount of Galium-68 remaining is; (2.5/2) mg

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If the mass of the original sample of Galium-68 is 10 mg, then . . .

== After one half-life, (1/2)(10 mg) = 5 mg remain

== After the second half-life, (1/2)(5 mg) = 2.5 mg remain

== After the third half-life, (1/2)(2.5 mg) = 1.25 mg remain

It doesn't matter how long the half-life is.