The Environmental Protection Agency and health officials nationwide are concerned about the levels of Radon gas in homes. The half-life of Radon-222 isotope is 3.8 days. If a sample of gas taken from
basement contains 4.38 ug of Radon-222, how long will it be until 0.55 ug will remain? How many half lives?

It takes 11.4 days⇒three half-lives

General formulas used in decay:  

T = duration of decay  

t 1/2 = half-life  

N₀ = the number of initial radioactive atoms  

Nt = the number of radioactive atoms left after decaying during T time  

t1/2=3.8 days

No=4.38 μg

Nt=0.55 μg

the density of gold = 19.3 g/cm3

the relation between density and mass and volume is

density = mass / volume

given :

mass of gold = 13 g

density = 13g / volume = 19.3

volume = 13 /19.3 = 0.67 cm^3

thus volume of gold nugget = 0.67 cm^3