Chapter 39, Problem 29A

Consider two 100-gram samples of radium-226 and uranium-238. Rank by the amount left of each.

(A) radium after 1620 years

(B) uranium after 2 half-lives

(C) radium after 3 half-lives

(D) uranium after 1 half-life

To determine

The rank of radioactive element by left amount of the Uranium and Radium.

Explanation of Solution

Introduction:

The amount of the radioactive elements becomes half the initial amount in the duration equal to the half-life of the radioactive element.

The half-life of radium is 1620 years. So, the amount becomes 50 gram in the sample of radium-226.

The amount of the uranium after two half-life becomes one-fourth of the initial amount. So, the 25 grams uranium is left in the sample of uranium-238.

The amount of the radium after three half-life becomes one-eighth of the initial amount. So, the 12.5 grams radium is left in the sample of radium-226.

The amount of the uranium after one half-life becomes half of the initial amount. So, the 50 grams uranium is left in the sample of uranium-238.

Conclusion:

Thus, the rank of samples by the amount of radioactive material left is A = D, B, C.