A radioisotope of technetium is useful in medical imaging techniques. A sample initially contains 80.0 mg of this isotope. After 24.0 h, only 5.0 mg of the technetium isotope remains. What is the half-life of the isotope?

a. 3.0 h

b. 6.0 h

c. 12.0 h

d. 16.0 h

e. 24.0 h

Option b. 6 h.

Explanation:

1) dа ta:

a) A₀ = 80.0 mg

b) A₁ = 5.0 mg

c) t = 24.0 h

2) Definition:

Half-life is the time required to decrease the initial amount of a sample of matter by half.

The half-life of each kind of radioisotope is a constant.

3) Solution:

The ratio of final mass to initial mass of the radioisotope is:

5.0 mg / 80.0 mg = 1 / 16 = (1 / 2) ⁴ = (1/2) * (1/2) * (1/2) * (1/2)

That shows that 4 half-lives have passed so that the isotope content has been reduced from 80.0 mg to 5 mg.

Since, the half-life is a constant, each half - life is equal to

24.0 h / 4 = 6 h, which is the option b.