Concise Physical Chemistry

c10 JWBS043-Rogers September 13, 2010 11:26 Printer Name: Yet to Come

PROBLEMS AND EXAMPLES 161

Time (ms)

0 50100150200250300350

Relative Intensity

0.0

0.2

0.4

0.6

0.8

1.0

1.2

FIGURE 10.7 First-order fluorescence decline from electronically excited iodine in mil-

liseconds.

The statistical routine of the SigmaPlot©C11.0 package gives, among other things,

Equation: Polynomial, Linear

f=y 0 +a*x

Coefficient Std. Error

y 0 0.0889 0.1232

a −0.0098 0.0007

The intercept, given here asy 0 , is close to 0 as it should be and the slope, given

here asa,is− 0 .0098 ms−^1. This leads to a rate constantdI/dt=−kIofk=

9. 8 × 10 −^3 ms−^1. The half-time for radiative decay is

t 1 / 2 =

ln 2

9. 8 × 10 −^3 ms−^1

=

. 693

9. 8 × 10 −^3 ms−^1

=71 ms

Time (ms)

0 100 200 300

ln

I^

-3.5

-3.0

-2.5

-2.0

-1.5

-1.0

-0.5

0.0

0.5

FIGURE 10.8 The natural logarithm of relative intensity vs. time for radiative decay. Within

experimental error, the plot is linear (Section 10.1).