# Estimating the Age of the Earth Using Uranium Decay

• says
In summary, by using the equation N = N0 - kt and knowing the half-life of U-238 and U-235, the age of the Earth can be estimated by calculating the decrease in U-235 over time. Assuming an even amount of both types of Uranium when the Earth was formed, the age of the Earth can be estimated to be around 4.2 billion years.
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.

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:
says said:

## 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

PietKuip said:
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.

PietKuip

## What is the estimated age of the Earth?

The current estimated age of the Earth is 4.54 billion years. This age is determined through various scientific methods, such as radiometric dating of rocks and analysis of the Earth's magnetic field.

## How do scientists estimate the age of the Earth?

Scientists use a variety of methods to estimate the age of the Earth, including radiometric dating, geological evidence, and analysis of meteorites. These methods involve studying the decay of radioactive elements, the formation and erosion of rocks, and the composition of the Earth's crust.

## What evidence supports the estimated age of the Earth?

There is a vast amount of evidence from different fields of science that supports the estimated age of the Earth. This includes geological evidence such as the layers of sedimentary rocks and the formation of mountains, as well as biological evidence from the fossil record and the evolution of species.

## Has the estimated age of the Earth changed over time?

Yes, the estimated age of the Earth has changed over time as new scientific techniques and evidence have been discovered. For example, in the 19th century, scientists estimated the Earth to be only a few million years old, but with advancements in technology and research, the current estimate is much older.

## Why is it important to estimate the age of the Earth?

Understanding the age of the Earth is crucial for understanding the history and evolution of our planet. It also allows us to better understand the processes that have shaped the Earth and can help predict future changes. Additionally, estimating the age of the Earth is important in the search for other habitable planets in the universe.

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