based on the half-life of Tc-99, how many half-lives have to pass for a 150 mg sample of Tc-99 to decay down to 30mg?

2.322 half-lives have passed to decay down from 150 miligrams to 30 miligrams.

Explanation:

The half of Technetium-99 is approximately 211000 years. The decay of isotopes is represented by the following ordinary differential equation:

(Eq. 1)

Where:

- First derivative of isotope mass in time, measured in miligrams per year.

- Mass of the isotope, measured in miligrams.

- Time constant, measured in years.

Now we proceed to obtain the solution of this differential equation:

(Eq. 2)

Where:

- Initial mass of the isotope, measured in miligrams.

- Time, measured in years.

The time passed for isotope is cleared within the equation described above:

In addition, we can obtain the time constant as a function of half-life:

(Eq. 3)

If we know that , and , then the time passed is:

The amount of passed half-lives is that time divided by a half-life. That is:

2.322 half-lives have passed to decay down from 150 miligrams to 30 miligrams.

they it depends on if one believes about radioactivity, they make a geiger counter beep but maybe it was going to beep anyway electronics do wierd things all the time or it was programmed to beep near certain metals.

elements make up everything, and they combine to make compounds.

the answer is c