What is the half-life in minutes of a radioactive nuclide?

Question

What is the half-life in minutes of a radioactive nuclide if 1 ⁄ 64th of the original sample remains after 116.0 min ?

Answer 1

Think about the definition of a half-life: the time it takes for one-half of the oringinal sample to have decayed into something else.

So, to get to 1/64th of the sample, how many half-lives have you used?

1 half life = ½ of the sample
2 half lives = ½ * ½ = ¼ of the sample
3 half lives = ½ * ½ * ½ = ⅛ of the sample
4 half lives = 1/16th
5 half lives = 1/32
6 half lives = 1/64

So, you've gone through 6 half lives.

116.0 / 6 = 19.33 minutes per half-life

Answer 2

0.5-existence equation is as follows: LN ( Nt a million/32 No ) = - ok * t Variable definitions: Nt - volume very last after the time period No - initial type of nuclei (at time 0) ok - decay consistent t - time period of deterioration because we do not have the decay consistent, we favor to apply the following equation in order to discover it: ok = LN(a million/32) a million/32 x x is the 0.5 existence (regularly denoted as "t^(5671f7d8e9aceba4344a40a5be46593f5671f7d8e9aceba4344a40a5be46593f5671f7d8e9aceba4344a40a5be46593f)") employing this on your question, we finally end up with the following equation: LN( [5671f7d8e9aceba4344a40a5be46593f5671f7d8e9aceba4344a40a5be46593f5671f7d8e9aceba4344a40a5be46593f5671f7d8e9aceba4344a40a5be46593f] a million/32 a million/32 ) = - ( LN(a million/32) a million/32 x ) * 5671f7d8e9aceba4344a40a5be46593f8.0 fixing for x we acquire a million/32.6 minutes as a nil.5-existence.

Answer 3

19.3333 min.