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Unformatted text preview: 38. Our approach (based on Eq. 2329) consists of several steps. The ﬁrst is to ﬁnd an approximate value of
e by taking diﬀerences between all the given data. The smallest diﬀerence is between the ﬁfth and sixth
values: 18.08 × 10−19 C − 16.48 × 10−19 C = 1.60 × 10−19 C which we denote eapprox . The goal at this
point is to assign integers n using this approximate value of e:
datum 1
datum 2
datum 3
datum 4
datum 5
datum 6
datum 7
datum 8
datum 9 6.563 × 10−19 C
eapprox
8.204 × 10−19 C
eapprox
11.50 × 10−19 C
eapprox
13.13 × 10−19 C
eapprox
16.48 × 10−19 C
eapprox
18.08 × 10−19 C
eapprox
19.71 × 10−19 C
eapprox
22.89 × 10−19 C
eapprox
26.13 × 10−19 C
eapprox = 4.10 =⇒ n1 = 4 = 5.13 =⇒ n2 = 5 = 7.19 =⇒ n3 = 7 = 8.21 =⇒ n4 = 8 = 10.30 =⇒ n5 = 10 = 11.30 =⇒ n6 = 11 = 12.32 =⇒ n7 = 12 = 14.31 =⇒ n8 = 14 = 16.33 =⇒ n9 = 16 Next, we construct a new data set (e1 , e2 , e3 . . .) by dividing the given data by the respective exact
integers ni (for i = 1, 2, 3 . . .):
(e1 , e2 , e3 . . .) = 6.563 × 10−19 C 8.204 × 10−19 C 11.50 × 10−19 C
,
,
...
n1
n2
n3 which gives (carrying a few more ﬁgures than are signiﬁcant)
1.64075 × 10−19 C, 1.6408 × 10−19 C, 1.64286 × 10−19 C . . .
as the new data set (our experimental values for e). We compute the average and standard deviation of
this set, obtaining
eexptal = eavg ± ∆e = (1.641 ± 0.004) × 10−19 C
which does not agree (to within one standard deviation) with the modern accepted value for e. The
lower bound on this spread is eavg − ∆e = 1.637 × 10−19 C which is still about 2% too high. ...
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This note was uploaded on 11/12/2011 for the course PHYS 2001 taught by Professor Sprunger during the Fall '08 term at LSU.
 Fall '08
 SPRUNGER
 Physics

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