Ineed

a rubidium isotope has a half-life of almost 50 billion years. given that scientists estimate earth's age to be 4.6 billion years, what is the most likely percentage of parent to daughter isotopes of this element currently existing on earth?

the ratio of parent to daughter =  15.38 : 1

Explanation:

The radioactive disintegration is considered to be first order reaction.

The relation between first order rate constant and the half life is:

Let us calculate the rate constant from half life as

The rate law expression for first order reaction is

Where

A0 = initial amount of rubidium isotope = say 100

At= final amount of rubidium isotope after 4.6 billion years

putting all values

1.065=100/At

At=93.897

The amount of daughter isotope formed =100-93.897 = 6.103

the ratio of parent to daughter = 93.897:6.103 = 15.38 : 1

n2(g) + 3h2-> 2nh3(g)   this is the balanced equation

note the mole ratio between n2, h2 and nh3.   it is 1 : 3 : 2   this will be important.

moles n2 present = 28.0 g n2 x 1 mole n2/28 g = 1 mole n2 present

moles h2 present = 25.0 g h2 x 1 mole h2/2 g = 12.5 moles h2 present

based on mole ratio, n2 is limiting in this situation because there is more than enough h2 but not enough n2.

moles nh3 that can be produced = 1 mole n2 x 2 moles nh3/mole n2 = 2 moles nh3 can be produced

grams of nh3 that can be produced = 2 moles nh3 x 17 g/mole = 34 grams of nh3 can be produced

note:   the key to this problem is recognizing that n2 is limiting, and therefore limits how much nh3 can be produced.