Assuming that at the beginning of time (big bang; creation of the universe) there

were equal numbers of U-235 and U-238 atoms produced, estimate the age of
the Earth (using terrestrial U-235 and U-238 abundances).

What does this have to do with health?

Here are the numbers you need to solve the problem:
U235 half life = T235 = 7.1*10^8 y
U238 half life = T238 = 4.51*10^9 y

Present value of the U235/U238 abundance 0.072 ratio =

i don't understand

What does this have to do with health?

Here are the numbers you need to solve the problem:
U235 half life = T235 = 7.1*10^8 y
U238 half life = T238 = 4.51*10^9 y

Present value of the U235/U238 abundance ratio = 0.0072

OK. Now solve this equation for the "age of the universe", T

(1/2)^(T/U235)/(1/2)^(T/U238) = 0.0072

(1/2)^[T*(1.41*10^-9 -0.22*10^-9]
= (1/2)^[(1.19*10^-9)T]= 0.0072
Lake logs of both sides.
[(1.19*10^-9)T]*(-0.301)) = -2.143
T = ____
Not a bad guess, but the actual value of the universe age is believed to be about twice as high.

Creationism notwithstanding

My first answer was accidentally sent before completion. I hope you can understand the complete version that I just uploaded

To estimate the age of the Earth using the terrestrial abundance of U-235 and U-238, we can use the principle of radioactive decay.

Uranium-238 (U-238) decays very slowly over time into lead-206 (Pb-206) through a series of intermediate isotopes. U-235 also decays into Pb-207 but at a faster rate. By measuring the ratio of lead isotopes to uranium isotopes in a sample, we can determine the age of the uranium-bearing mineral or rock.

The natural abundance of U-235 and U-238 can be used to calculate the initial ratio of U-235 to U-238 in the Earth's crust. The vast majority of uranium in the Earth's crust consists of U-238, with only a small fraction being U-235 (99.27% U-238 and 0.72% U-235).

For the purposes of this calculation, we will assume that the Earth initially had equal ratios of U-235 and U-238, which means 50% of the total uranium was U-235 and the other 50% was U-238.

Now, let's use the concept of half-life to estimate the age of the Earth:

1. Start with the assumption that at the beginning (t=0), 50% of the total uranium was U-235 and 50% was U-238.

2. Since we know the half-life of U-235 is approximately 704 million years, we can calculate how many half-lives have passed since the formation of the Earth.

3. Divide the age of the Earth (in years) by the half-life of U-235 to find the number of half-lives that have passed.

4. Multiply the number of half-lives by the half-life of U-235 to get the age of the Earth.

It is important to note that this method provides an estimate because there could have been variations in the initial U-235 to U-238 ratio and radioactive decay rates. Additionally, this calculation assumes that there has been no significant loss or gain of uranium or lead from the Earth's crust since its formation.

Based on current scientific knowledge, the estimated age of the Earth is approximately 4.54 billion years using various dating methods, which aligns with our understanding of the formation of the solar system.