Estimating the Age of the Earth Using Uranium Decay

[says]

Homework Statement

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.

Homework Equations

N = N₀ - kt

where
N = amount after time t
N₀ = amount at time=0
k = decay constant
t = time

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.

 

[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

 

[SteamKing]

Homework Statement

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.

Homework Equations

N = N₀ - kt

where
N = amount after time t
N₀ = amount at time=0
k = decay constant
t = time

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.

What you are missing is that the rate of decay is proportional to the amount of substance on hand at anyone 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

 

[SteamKing]

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 %.

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