Rutherford once assumed that when the earth was first formed, it contained equal amounts of u-235 and u-238. from this, he was able to determine the age of the earth. find the rutherford age of the earth.

Explanation:

As the radioactive decay is an exponential decay, lets first remember how to solve an exponential decay problem.

In an exponential decay the quantity of substance N at time t is given by:

where is the initial quantity of substance and is the mean lifetime of the substance.

For our problem we start with the same quantity of U-235 and U 238. Lets call this quantity as .

The quantity of U-235 after a time t will be:

and for U-238

Lets call the ratio between this two r. r will be:

Now, in the present time the abundance of U-235 is 0.720% and the abundance of U-238 is 99.274%. This gives us a ratio of:

the mean lifetime of U-235 is

and the mean lifetime of U-238 is

so

Taking all this in consideration, we get:

would be false hope this out

lol

explanation: