Question

PLEASE!!! I NEED HELP ASAP!!

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?

Answer 1

w=m₁/m₀=2^(-t/T)

t=4.6·10⁹ years
T=5·10¹⁰ years

w=2^(-4.6·10⁹/5·10¹⁰)

w=0.9382
w=93.82%

Answer 2

the ratio of parent to daughter = 15.38 : 1

Step-by-step explanation:

The radioactive disintegration is considered to be first order reaction.

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

`k=\frac{0.693}{t_{(1)/(2) }}`

Let us calculate the rate constant from half life as

`k=(0.693)/(50)=0.01386 (billionyr)^(-1)`

The rate law expression for first order reaction is

`kt=ln([A0])/(At)`

Where

A0 = initial amount of rubidium isotope = say 100

At= final amount of rubidium isotope after 4.6 billion years

putting all values

`0.1386X4.6=ln(100)/(At)`

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