Use the following half-life graph to answer the following question:

a graph titled half-life graph of a radioactive isotope is shown with mass remaining on the y axis from 0 to 60 grams and time on the x axis from o to 6 minutes. a curve connects the points 0, 50 and 1, 25 and 2, 12.5 and 3, 6.25 and 4, 3.125 and 5, 1.562.

the graph is attached.

when you are left with 6.25 mg of the radioactive isotope, how many half-lives have occurred from time equals zero? (5 points)

a. 1

b. 3

c. 6

d. 12

B. 3

Explanation:

The half-life of a radioisotope is the time it needs for the mass of the radioisotope to halve with respect to its original value.

In this problem, the initial mass of the radioisotope at t=0 is

m0 = 50.0 mg

We see that after t = 1 min, the mass of the isotope is

m(1 min) = 25.0 mg

so, exactly half the initial mass: this means that 1 minute is exactly the half-life of this radioisotope.

So, the amount of mass left after each minute is the following:

m (1 min ) = 25.0 mg (1 half-life)

m (2 min) = 12.5 mg (2 half-lives)

m (3 min) = 6.25 mg (3 half-lives)

so, when we are left with 6.25 mg of isotope, 3 minutes have passed, which means that 3 half-lives have passed.

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