Uranium-238 decays to Lead-206. The half life of Uranium-238 is 4.5 billion years. If you have a 100 g sample. How much sample will you have after 2 half lifes?

just do it in your head ...

after 1 half-life you would have 50 g left
after 2 half-lifes you would have 25 g left

Your question isn't quite clear to me. If you want the mass of U after two half lives, then 25 g is correct. If you want the mass of sample left after two half lives, that is 25g U + the equivalent of 75 g U that's been converted to Pb. That conversion is 75 g U x (atomic mass Pb/atomic mass U) = about 75*207/238 = about 65 g. Therefore, the total mass is 25 + about 65 = about 90 g.

If the half-life of a radionuclide is 1 month, is a sample of it completely decayed after 2 months?

4.5 ×1o ^ 9

To determine the amount of sample remaining after a certain number of half-lives, we can use the formula:

Remaining Sample = Initial Sample * (1/2)^(Number of Half-lives)

In this case, the initial sample is 100 g, and we want to find the sample remaining after 2 half-lives. The half-life of Uranium-238 is given as 4.5 billion years.

To calculate the sample remaining after 2 half-lives, we need to divide the time in years by the half-life:

Time in years = Number of Half-lives * Half-life

Time in years = 2 * 4.5 billion years

Time in years = 9 billion years

Now we can substitute the values into the formula:

Remaining Sample = 100 g * (1/2)^(9 billion years / 4.5 billion years)

Simplifying further:

Remaining Sample = 100 g * (1/2)^2

Remaining Sample = 100 g * (1/4)

Remaining Sample = 25 g

Therefore, after 2 half-lives, you will have 25 grams of the sample remaining.