Question

Radioactive radon-222, found in many homes, is a potential health hazard. The half-life of radon-222 is 3.82 days. If you begin with 35.3 mg of this isotope, what mass remains after 10.1 days have passed

Answer 1

5.65mg of the isotope remains

Step-by-step explanation:

The radioactive decay follows the equation:

Ln[A] = -kt + ln[A]₀

Where [A] is amount of the isotope after time t, k is decay constant, and [A]₀ is initial amount of the isotope.

k = ln 2 / Half-life

k = ln 2 / 3.82 days

k = 0.18145days⁻¹

Replacing:

Ln[A] = -0.18145days⁻¹*10.1days + ln[35.3mg]

ln[A] = 1.7312

[A] = 5.65mg of the isotope remains