Estimate the age of the Earth

1. Dec 11, 2015

says

1. The problem statement, all variables and given/known data
The half life of U-238 is approximately 4.4 billion years, while U-235 is approximately 700,000,000.

A Uranium ore has 0.75% U-235.
Assuming there was an even amount of both types of Uranium when the Earth was formed, estimate the age of the Earth.

2. Relevant equations
N = N0 - kt

where
N = amount after time t
N0 = amount at time=0
k = decay constant
t = time
3. The attempt at a solution
I don't do a lot of derivation at my school, but I want to get a lot better at it.

N = N0 - kt

dN / dt = -kt

dN = -kt dt

∫ - kt dt (definite integral from t to t0

= -k(t - t0)

I'm not really sure to go from here.

2. Dec 11, 2015

PietKuip

Maybe they are asking for a crude estimate?
So 1.4 My ago there was four times as much U-235, about 3 %.
And 4.2 My ago there was 64 times as much. But back then there was also twice as much U-238, so the U-235 content was about 25 %.

PS: Should be Gy. Thanks SteamKing

Last edited: Dec 11, 2015
3. Dec 11, 2015

SteamKing

Staff Emeritus
What you are missing is that the rate of decay is proportional to the amount of substance on hand at any one time:

https://en.wikipedia.org/wiki/Exponential_decay

Knowing the rate of decay allows you to calculate the half-life of the substance:

https://en.wikipedia.org/wiki/Half-life

4. Dec 11, 2015

SteamKing

Staff Emeritus
If by 'My' you mean billions (109) of years.