# The first-order decay of radon has a half-life of 3.823 days. How many grams of radon decompose after 5.55 days if the sample initially weighs 100.0 grams?

##### 1 Answer

Oct 16, 2016

After 5.55 days, 63.4 g of radon will have decayed.

#### Explanation:

The formula for the half-life of a first-order process is

#color(blue)(bar(ul(|color(white)(a/a) t_½ = (ln2)/kcolor(white)(a/a)|)))" "#

∴

The integrated formula for a first-order process is

#color(blue)(bar(ul(|color(white)(a/a) ln"A"_0 - ln"A" = ktcolor(white)(a/a)|)))" "#

If 36.55 g remain, the mass that decomposed is