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Rufina [12.5K]
3 years ago
6

In 8,450 seconds, the number of radioactive nuclei decreases to 1/16 of the number present initially. What is the half-life (in

s) of the material
Physics
1 answer:
almond37 [142]3 years ago
7 0

Answer:

<h2>2113 seconds</h2>

Explanation:

The general decay equation is given as N = N_0e^{-\lambda t} \\\\, then;

\dfrac{N}{N_0} = e^{-\lambda t} \\ where;

N/N_0 is the fraction of the radioactive substance present = 1/16

\lambda is the decay constant

t is the time taken for decay to occur = 8,450s

Before we can find the half life of the material, we need to get the decay constant first.

Substituting the given values into the formula above, we will have;

\frac{1}{16} = e^{-\lambda(8450)}  \\\\Taking\ ln\ of \both \  sides\\\\ln(\frac{1}{16} ) =  ln(e^{-\lambda(8450)})  \\\\\\ln (\frac{1}{16} )  = -8450 \lambda\\\\\lambda = \frac{-2.7726}{-8450}\\ \\\lambda = 0.000328

Half life f the material is expressed as t_{1/2} = \frac{0.693}{\lambda}

t_{1/2} = \frac{0.693}{0.000328}

t_{1/2} = 2,112.8 secs

Hence, the half life of the material is approximately 2113 seconds

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