Which radioactive sample would contain the greatest remaining mass of the radioactive isotope after 10 years?

A. 2.0 grams of 198 Au
B. 2.0 grams of 42 K
C. 4.0 grams of 32 P
D. 4.0 grams of 60 Co

By the way the numbers next to the elements are their atomic masses. thanks again

You must look up the half-life of each of the isotopes. Surely you have a text or notes that will furnish this. Co-60 is the only one I know from memory for I worked with it many years ago. It is 5.1 years half-life. Then half of the mass will remain after 1 half life, 1/4 will remain after two half lives, etc.
You can also use
ln(No/N)=kt I can help with that if you need help after you obtain the half lives.

It is D

4.0 grams of 60Co

It is choice (D)

4.0 grams of 60Co

Plz dont cheat! Just learn!

It will help you in the long run...

A. 2.0 grams of 198 Au - Sorry, I can't make any jokes about this option. It's pretty "Au"ful.

B. 2.0 grams of 42 K - As much as I love bananas, I have to say this option is a "K"atastrophe.

C. 4.0 grams of 32 P - That's a lot of "P"! But will it remain for long?

D. 4.0 grams of 60 Co - Ah, Co-60, the classic radioactive isotope! That's the "Co"-rrect choice.

The half-life of Cobalt-60 is around 5.1 years. So, after 10 years, we're looking at about 2 half-lives. Since half of the mass remains after each half-life, we're left with approximately 2 grams of 60 Co.

Therefore, the answer is D. 4.0 grams of 60 Co. It's a "Co"mically clear winner!

To determine which radioactive sample would contain the greatest remaining mass of the radioactive isotope after 10 years, we need to compare the half-lives of each isotope.

The half-life of an isotope is the amount of time it takes for half of the radioactive substance to decay. Based on the information given, we need to look up the half-life for each isotope:

A. 198Au (Gold) - Look up the half-life of 198Au. Let's say its half-life is T1.
B. 42K (Potassium) - Look up the half-life of 42K. Let's say its half-life is T2.
C. 32P (Phosphorus) - Look up the half-life of 32P. Let's say its half-life is T3.
D. 60Co (Cobalt) - The half-life of 60Co is 5.1 years.

To evaluate the remaining mass after 10 years, we need to calculate the number of half-lives that have occurred. This can be done using the formula:

n = t / T

Where:
- n is the number of half-lives that have occurred,
- t is the time elapsed (10 years in this case),
- T is the half-life of the isotope.

Calculate n for each isotope:

For 198Au: n1 = 10 / T1
For 42K: n2 = 10 / T2
For 32P: n3 = 10 / T3
For 60Co: n4 = 10 / 5.1

Now, calculate the remaining mass using the formula:

Remaining mass = Initial mass * (1/2)^n

For each isotope:

For 198Au: Remaining mass1 = 2.0 grams * (1/2)^n1
For 42K: Remaining mass2 = 2.0 grams * (1/2)^n2
For 32P: Remaining mass3 = 4.0 grams * (1/2)^n3
For 60Co: Remaining mass4 = 4.0 grams * (1/2)^n4

Compare the remaining masses for each isotope. The isotope with the greatest remaining mass after 10 years would be the answer.