help with radon

Question

  radon is a naturally occurring radioactive gas.  it is one of the products produced as uranium decays.  radon has half-life of approximately 4 days.  if you have a sample of radon with a mass of 4 grams, how many grams will be left at the end of 8 days.

 

a.  4

 

b.  2

 

c.  1

 

d.  none of these

 

thank you

Answer 1

Every 4 days, the amount of radon you started with is reduced by half.

 

Start with 4 grams of radon on day 1

 

After 4 days, you have (1/2)* 4 grams of radon = 2 grams

 

Start with 2 grams of radon on day 5

 

After four more days (end of day 8) you have:

 

(1/2)*2 grams = ?

 

---------------------------

 

The general formula is R = R₀*(1/2)^d/4

 

Where R₀ is the amount of radon you start with on the first day, d is days, and R is the amount you have left after d days.

 

So for your case, R₀=4 grams and d = 8 days:

 

R = (4)(1/2)^8/4 = (4)(1/2)² = (4)(1/4) = ?