The half-life of 232-th is 1.4 x 10^10 years. if there were 25.0 grams of thr sample left after 2.8 x 10^10 years, how many grams were in the orifinal sample

1.    For this problem, we use the formula for radioactive decay which is expressed as follows:

An = Aoe^-kt

where An is the amount left after time t, Ao is the initial amount and k is a constant. 

We calculate as follows:

An = Aoe^-kt
0.5 = e^-k(1.4x10^10)
k = 4.95x10^-11

An = Aoe^-kt
25 = Aoe^-4.95x10^-11(2.8x10^10)
Ao = 100 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.