Question

The following data were collected for a phosphorescent paint being proposed for use in coating highways. Time Intensity (s) (lux) 10 1528 20 768 386 194 97 49 25 12 6 30 40 50 60 70 80 90 100
Calculate the half-life of the paint (in seconds).

What is the intensity of the light at the 2nd half-life?

What is the intensity of the light at the 3rd half-life?
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Answer #1

We will plot a graph between ln(intensity) and time

intensity In (intensi 1528 7.331715 768 6.64379 386 5.955837 194 5.267858 97 4.574711 493.89182 25 3.218876 12 2.484907 6 1.7

intensity at first half life =?

ln [I] = -0.069 X 10.04 + 8.034 = 7.34

[I] = 1540.7

Second half life is when the intensity is half of this

[I] = 1540.7 / 2 = 770.35

So second half life will be calcualted from

y = -0.069x + 8.034

ln [770.35] = -0.069 x + 8.034

1.384 / 0.069 = 20.05 seconds

The third half life is when the intensity is half of second half life = 770.5/2 = 385.25

y = -0.069x + 8.034

ln[385.25] = -0.069x + 8.304

x = third half life = 34.05 seconds

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