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# If 100 g of Au-198 decays to 6.25 g in 10.8 days, what is the half-life of Au-198?

Dec 20, 2016

Half life of 2.7 days

#### Explanation:

Since Au-198 is 100 g originally and it decays to 6.25 g,

You'd divide 100 g by 2 until you reach 6.25 g:

$\frac{100}{2} = 50$; $\frac{50}{2} = 25$; $\frac{25}{2} = 12.5$; $\frac{12.5}{2} = 6.25$

Since there were four 2s, divide 10.8 days by 4:

$\text{10.8 days"/4 = "2.7 days}$

100 g of Au-198 would have a half life of 2.7 days.