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The radioactive element americium-241 decays at a rate of 0. 1604%. How many years will it take a 20-g mass of americium-241 to decay to 7. 2 g? Round your answer to the nearest year. (Hint: make sure to change your percentage to a decimal. )

User Thales MG
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The decay of americium-241 follows an exponential decay model, so we can use the formula:

A = A0*e^(-kt)

where:
A0 = initial amount of americium-241 (20 g in this case)
A = amount of americium-241 after time t
k = decay constant (we can find it from the given decay rate)
t = time (in years)

The decay rate is 0.1604%, which is equivalent to 0.001604 as a decimal.

We can use the fact that when the mass decays to 7.2 g, the remaining mass is 7.2 g and the initial mass was 20 g. So we can write:

7.2 = 20*e^(-0.001604t)

Divide both sides by 20:

0.36 = e^(-0.001604t)

Take the natural logarithm of both sides:

ln(0.36) = -0.001604t

Solve for t:

t = -ln(0.36)/0.001604

t ≈ 114.5

Rounding to the nearest year, it will take about 115 years for a 20 g mass of americium-241 to decay to 7.2 g.
User Sonali Das
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