Question

If you start with 65 milligrams of chromium 51, used to track red blood cells, which has a half-life of 27.7 days, how long will it take for 80% of the material to decay?

A) 55.4 days
B) 55.6 days
C) 55.8 days
D) 56.0 days

Answer 1

To find how long it will take for 80% of the material to decay, we can use the concept of half-life. The half-life of chromium-51 is 27.7 days, so we can set up an equation with the desired decay amount and solve for the number of half-lives. Then, we can multiply the number of half-lives by the length of one half-life to find the total time.

Step-by-step explanation:

To find how long it will take for 80% of the material to decay, we can use the concept of half-life. The half-life of chromium-51 is 27.7 days, meaning that it takes 27.7 days for half of the material to decay. We want to know how long it will take for 80% (or 0.8) of the material to decay, so we can set up the following equation:

0.5^n = 0.8, where n is the number of half-lives.

Taking the logarithm of both sides, we get:

n = log0.5(0.8)

Using a calculator, we find that n is approximately 1.736. Since each half-life is 27.7 days, we can multiply n by 27.7 to find the total time:

1.736 * 27.7 = 55.4952

Rounding to the nearest day, it will take approximately 55.5 days for 80% of the material to decay.