The half-life of gold-198 is 2.77 days
Given:
mass of gold sample = 200-gram
mass of decay sample = 160 grams
time taken to decay = 6.25 days
To Find:
the half-life of gold-198
Solution: The amount of time it takes to disintegrate by half an initial amount. For a given reaction, a reactant's half-life t1/2 is the time it takes for its concentration to reach a value which is the arithmetic mean of its initial and final (equilibrium) value.
Since Au-198 is 200 g originally and it decays to 160 g, so 40g left
the fraction decay is 40/200 = 0.2
the time base is 6.25 days
ln0.2/6.25 = -0.25
k=ln2/half life therefore half-life = ln2/k = ln2/0.25
half life = 2.77 days
So, half life of gold is 2.77 days
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