Asample taken from a layer of mica in a canyon has 2.10 grams of potassium-40. a test reveals it to be 2.6 billion years old. how much potassium-40 was in the sample originally if the half-life of potassium-40 is 1.3 billion years?

Explanation:

The half-life of K-40 (1.3 billion years) is the time it takes for half of it to decay.  

After one half-life, half (50 %) of the original amount will remain.  

After a second half-life, half of that amount (25 %) will remain, and so on.  

We can construct a table as follows:  

 No. of                                 Fraction

half-lives          t/yr             Remaining  

      0               0                          1

      1                1.3  billion              ½

      2              2.6                          ¼

      3              3.9                          ⅛

We see that after 2 half-lives, ¼ of the original mass remains.

Conversely, if two half-lives have passed, the original mass must have been four times the mass we have now.

Original  mass = 4 × 2.10 g =

the density(ratio between mass and volume as m/v) decreases from top to bottom in periodic table group as the size increases and nuclear charge decreases. but in periods density increases from left to right as atom size decreases and nuclear charge increases.