What is the half life of an isotope that decays to 50 percent of its original activity on 40.9 hours?

Answer 1

15 days

Answer 2

11.2 hours

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You get it as a solution of the equation:

0.25 = e (-0.693 x 22.4/ half life)

or

half life = 0.693 x 22.4/ln 4 hours

Answer 3

If it takes 40.9 hours for 50% of the original activity to decay, then the half-life is 40.9 hours. That is what half-life means: the length of time it takes for 50% of the activity to decay. What may be confusing to some is that, in the second half-life, i.e. the next 40.9 hours, half of the half, i.e. 25% will decay, and then 12.5%, and so on and so forth.

The equation for half-life is...

AT = A0 2(-T/H)

... where A0 is the starting activity, AT is the activity after some time T, and H is the half life in units of T. There are other variations of this equation, some involving powers of e, some involving powers of 10. I like this version because, with the inverse power of 2, it is clear and easy to remember, and I don't need to remember any 0.693 factors, and stuff like that.

Answer 4

14.06 hours