# Rate of Decay Formula

The rate of decay for radioactive particles is a first order decay process. This means it follows an exponential decay pattern which can be easily calculated.

N_{t} = the amount of radioactive particles are time (t)

N_{0} = the amount of radioactive particles at time = 0

t = time

Taking the natural log of both sides of this equation (remember it is an exponential decay) will yield:

Rate of Decay Formula Questions:

1. Calculate the rate of decay constant for U-238 if its half-life is 4.468 × 10^{9} years.

Answer:

If the problem is referring to the half-life, then the ratio of = 0.5 because half of the original sample has already undergone decay.

1.55 x 10^{-10} years^{-1} =λ

2. Calculate how long it will take for 25% of a U-238 sample to radioactively decay.

Answer:

If 25% of the sample has undergone radioactive decay, then the ratio of = 0.75 because 75 percent of the original sample remains. The rate of decay constant for U-238 will be used from the previous problem.

1.86 x 10^{9} years = t

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